Methods and apparatus for high resolution imaging with reflectors at staggered depths beneath sample

ABSTRACT

A sample may be illuminated in such a way that light passes through the sample, reflects from a set of reflectors, passes through the sample again and travels to a light sensor. The reflectors may be staggered in depth beneath the sample, each reflector being at a different depth. Light reflecting from each reflector, respectively, may arrive at the light sensor during a different time interval than that in which light reflecting from other reflectors arrives—or may have a different phase than that of light reflecting from the other reflectors. The light sensor may separately measure light reflecting from each reflector, respectively. The reflectors may be extremely small, and the separate reflections from the different reflectors may be combined in a super-resolved image. The super-resolved image may have a spatial resolution that is better than that indicated by the diffraction limit.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/791,025 filed on Oct. 23, 2017, which claims the benefit of U.S.Provisional Application No. 62/411,586, filed on Oct. 22, 2016 (the“Provisional Application”). The entire disclosure of the ProvisionalApplication is herein incorporated by reference.

FIELD OF TECHNOLOGY

The present invention relates generally to imaging systems.

COMPUTER PROGRAM LISTING

The following five computer program files are incorporated by referenceherein: (1) extend.txt with a size of about 380 bytes; (2) getFFT.txtwith a size of about 619 bytes; (3) getThzSuperRes_InterweaveMC.txt witha size of about 575 bytes; (4) InterweaveR.txt with a size of about 266bytes; and (5) Thz_Subwavelength.txt with a size of about 11,212 bytes.Each of these five files was created as an ASCII .txt file on Oct. 8,2017.

BACKGROUND

Diffraction creates a limit on imaging resolution. This limit issometimes called the diffraction barrier. The diffraction barrier for agiven imaging system is determined by the optics of the imaging system.

Spatial Resolution: For a conventional imaging system with a numericalaperture NA, two point sources of equal intensity light can be spatiallyresolved by the system only if the distance between the centers of twospots of light (formed in the image plane by light from the two pointsources) is equal to at least the Abbe X-Y Resolution. As used herein,“Abbe X-Y Resolution” means λ/2NA, where NA is numerical aperture of theimaging system, and is wavelength. Thus, for any given imaging systemwith a given numerical aperture, Abbe X-Y Resolution is a limit, imposedby the physical laws of diffraction, on the system's spatial resolutionthat can be achieved by conventional optics.

SUMMARY

In illustrative implementations of this invention, an imaging system mayhave a spatial resolution that is better than its Abbe X-Y Resolution.That is, in illustrative implementations of this invention, the systemmay spatially resolve two locations in a sample being imaged, eventhough the two locations are so close together that: (a) lightreflecting directly back from the two locations in the sample forms twodisks of light in the image plane of the system; and (b) the centers ofthe disks are closer together than the system's Abbe X-Y Resolution.

In illustrative implementations, this dramatically improved spatialresolution is achieved by using light that reflects from a set ofreflectors located at staggered depths beneath the sample (instead oflight that reflects directly from the sample) and by taking advantage ofthe ultrafast time resolution of the system. Together, the reflectorsand ultrafast time resolution allow the imaging system to “work around”the diffraction barrier.

In illustrative implementations, the reflectors are staggered in depthbeneath the sample, in such a way that light reflecting back from thereflectors arrives at a light sensor during a different time intervalfor each reflector. The light sensor may have ultrafast temporalresolution. Thus, the light sensor may temporally resolve—that is,measure separately during different time intervals—the reflections thatarrive at different times from different reflectors. The light sensormay thus acquire a set of separate measurements, each of which,respectively, measures light that reflected from a particular reflectorduring a particular time interval. The system may then computationallycombine these separate measurements to create a spatially super-resolvedimage.

In illustrative implementations, extremely small reflectors are locatedbeneath the sample being imaged. Each reflector is at a different depth.Horizontally, the reflectors may be arranged in a closed-packedconfiguration, such as a 2×2 array, 3×3 array or closed-pack set ofthree reflectors.

In illustrative implementations, light that reflects back from thereflectors (through the sample) arrives at the light sensor at differenttimes for different reflectors (the greater the depth of the reflector,the longer it takes for light to return from the reflector).

In some implementations, a pair of points in the sample may be locatedso close to each other that the diffraction barrier would prevent aconventional camera from spatially resolving them. However, inillustrative implementations of this invention, if the points aredirectly above two reflectors (so that each of the points is directlyabove a different reflector), then the system may (despite thediffraction barrier) spatially resolve these two points. This is becausethe light sensor may have a sufficiently fast temporal resolution thatit may separately measure the reflection from each reflector,respectively (thereby taking advantage of the fact that reflections fromdifferent reflectors arrive during different time intervals). The systemmay computationally combine the separate measurements that were takenduring different time intervals into a single, spatially super-resolvedimage.

In this super-resolved image, there may be a spatially resolved,separately measured light intensity for the tiny x-y region of thesample that is directly above each reflector, respectively—even thoughthe tiny x-y regions that correspond to the reflectors may be so smallthat the diffraction barrier would ordinarily prevent them from beingspatially resolved. Again, this is because a separate measurement may betaken for each reflector (and its corresponding tiny x-y area of thesample), respectively. This ability to measure light from each reflector(and its corresponding tiny x-y region of the sample) separately mayarise because: (a) for each reflector, light that reflects from thereflector passes through a corresponding tiny x-y region of the sample(while traveling to and from the reflector); (b) the reflectors arestaggered in depth in such a way that light from each reflector (and itscorresponding x-y region of the sample), reaches the light sensor of thesystem during a different time interval; and (c) the light sensor takesa separate measurement during each of these different time intervals.Thus, there may be a separate measurement of light that reflects fromeach reflector (and its corresponding x-y area of the sample),respectively. Then the separate measurements taken at the separate timesmay be computationally combined to generate a spatially super-resolvedimage.

In some cases, the separate measurements for each reflector may beacquired by separating data in post-processing. For example, in somecases, the light sensor may take measurements of reflections over alonger period of time, and then, in post-processing, the system mayseparate the measurements into shorter time windows, in such a way thateach time window corresponds to a time interval in which light from aparticular reflector is expected to arrive at the light sensor. Forexample, in some cases: (a) the light sensor may, for a given positionon the sample that is directly above a particular reflector, take a 1Dvector of measurements over a longer time period (in which light fromall of the reflectors reaches the light sensor); and (b) the system maymultiply the 1D vector by a mathematical window function thatcorresponds to a time window in which light from that particularreflector is expected to arrive at the light sensor.

In illustrative implementations, the system may operate withoutswitchable fluorophores and without near field scanning probes.

This invention is well-suited for high-resolution imaging at lowerfrequencies (e.g., terahertz or infrared) where the wavelength islonger. For example, many materials have uniquely identifiable featureswhen imaged with terahertz light (such as certain explosives, narcotics,and polymorphic forms of compounds used in drugs). Conventionalterahertz imaging tends have low spatial resolution because of (amongother things) the longer wavelength of light in the terahertz range.Thus, this invention's ability to acquire super-resolved images in theterahertz range is highly desirable.

For example, in some implementations, the imaging system may employterahertz time-domain spectroscopy (“THz-TDS) to capture time-resolvedimages of a temporal sequence of terahertz pulses from the reflectors.

Alternatively, in some implementations, the imaging system may employoptical coherence tomography (“OCT”) to capture time-resolved images ofa sequence of pulses reflecting from the reflectors. Or, the imagingsystem may employ OCT to acquire separate measurements of CW (continuouswave) or other non-pulsed light reflecting from each reflector,respectively. The OCT system may separate the CW (or non-pulsed) lightthat reflects from different reflectors based on the phase of the light(because the phase of the light depends on the round-trip distance thatthe light travels, which in turn depends on the depth of the reflectors,and thus the phase will be different for each of the reflectors,respectively). In some cases, the OCT imaging system may operate withlight in the infrared range or in the visual spectrum.

This invention has many practical applications, including, among otherthings, super-resolved microscopy imaging, remote sensing, biomedicalimaging, industrial noninvasive inspections, water profilometery, andhyperspectral imaging (e.g., in the 5 GHz-500 GHz range of frequencies)

The Summary and Abstract sections and the title of this document: (a) donot limit this invention; (b) are intended only to give a generalintroduction to some illustrative implementations of this invention; (c)do not describe all of the details of this invention; and (d) merelydescribe non-limiting examples of this invention. This invention may beimplemented in many other ways. Likewise, the description of thisinvention in the Field of Technology section is not limiting; instead itidentifies, in a general, non-exclusive manner, a field of technology towhich some implementations of this invention generally relate.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1A shows a perspective view of a 2×2 array of reflectors.

FIGS. 1B, 1D, 1E and IF each show a top view of a set of reflectors.

FIG. 1C shows a side view of a set of reflectors.

FIGS. 1G and 1I each show a reflector that comprises a flat end of anelongated structure.

FIGS. 1H and 1J show cross-sectional views of the elongated structuresin Figures IG and 1I, respectively.

FIG. 2A shows hardware for a THz-TDS imaging system that includesreflectors at staggered depths beneath the sample.

FIG. 2B shows reflectors that have a circular cross-section.

FIGS. 3A and 3B are images of light reflecting from reflectors.

FIG. 3C is an image of light reflecting from a sample and fourreflectors.

FIG. 3D shows an HSV color map that is employed in FIGS. 3A-3C.

FIGS. 4A, 4B, 4C, and 4D are x-y images of light reflecting from fourdifferent reflectors, respectively.

FIG. 4E is an x-y-z image of light reflecting from four reflectors.

FIG. 4F is a JET color map that is employed in FIGS. 4A-4E.

FIGS. 5A and 5B are charts of measurements taken by a single pixel of aTHz-TDS detector.

FIG. 6A is an image formed by THz light that reflected directly from asample, and did not pass through the sample to the reflectors beneath.

FIG. 6B is an image formed by THz light that reflected internally withinthe sample.

FIGS. 6C-6F are images formed by THz light that was emitted by a THz-TDSspectrometer, then passed through the sample, then reflected from areflector, and then passed through the sample again. In FIGS. 6C, 6D,6E, 6F, the light reflected from a first, second, third and fourthreflector, respectively.

FIG. 6G is a super-resolved image.

FIG. 7 is a flow-chart of a method for THz-TDS imaging which employs aset of reflectors that are staggered in depth beneath a sample.

FIG. 8 is a flow-chart of a method for creating a super-resolved imageof a sample, by processing THz-TDS measurements of light that hasreflected from a set of reflectors that are staggered in depth beneaththe sample.

FIG. 9 shows hardware for an OCT imaging system that includes reflectorsstaggered at different depths beneath the sample.

FIG. 10 is a flow-chart of a method for OCT imaging which employs a setof reflectors that are staggered in depth beneath a sample.

FIG. 11 is a flow-chart of a method for creating a super-resolved imageof a sample, by processing OCT measurements of light that has reflectedfrom a set of reflectors that are staggered in depth beneath the sample.

The above Figures show some illustrative implementations of thisinvention, or provide information that relates to those implementations.The examples shown in the above Figures do not limit this invention.This invention may be implemented in many other ways. The Figures arenot necessarily drawn to scale.

DETAILED DESCRIPTION

Time Resolution/Depth Resolution

In illustrative implementations of this invention, the light sensor hasan ultrafast time resolution.

In illustrative implementations, this time resolution is so fast that itallows the light sensor to take separate measurements of reflectionsarriving from different reflectors at different times.

In illustrative implementations, time gating may be employed to achievethe ultrafast time resolution. The time gating may cause the imagingsystem to take measurements during only very short time windows, and notto take measurements during other periods. The time gating may beachieved in a wide variety of ways, depending on the particularimplementation of this invention. For example, in some cases, the timegating is performed by an opto-electronic switch, by a detection pulse,by a periodic timer gate, or in post-processing.

In some implementations, an optoelectronic switch is employed for timegating. The optoelectronic switch may detect an external triggeringevent and then cause the system to take measurements during a shortperiod of time after the triggering event. Then the system may revert tothe “off” state (in which it does not take measurements) until theswitch detects another external triggering event. For example, in somecases, an optoelectronic switch may detect an incoming pulse of light,and may cause the system to take measurements during the pulse, and thenthe system may revert to an “off” state, waiting for the switch todetect the next pulse. Or, for example, the triggering event detected bythe switch may be the arrival of light that has a particular phase(corresponding to a particular depth and thus to a particularreflector).

In some implementations, a detection pulse in a THz-TDS spectrometer isemployed for time gating. The THz-TDS spectrometer may emit a terahertzpulse to illuminate the sample. A portion of this pulse (called the“detection pulse”) may be diverted to an optical delay line and thensteered into the detector of the spectrometer. The detection pulse may(due to being delayed in the optical delay line) arrive in the detectorat the same time as the reflected pulse from the sample. The arrival ofthe detection pulse in the detector may trigger the detector to takemeasurements during an extremely short period of time in which thereflected pulse from the scene is incident at the detector.

In some implementations, the time gating is performed inpost-processing. For example, an imaging system may take measurements oflight over a period of time, but the system may discard themeasurements, unless they occur during a very short time period after atriggering event (that is detected in the measurements) occurs. Again,for example, the triggering event may be a pulse of light or may be aparticular phase of light or range of phases of light.

In some implementations, time gating is performed by a periodic timergate. This gate may—without attempting to detect an externaltrigger—periodically cause an ultrashort measurement to occur.

In illustrative implementations, the temporal resolution of the imagingsystem and its depth resolution are equivalent. This is because, in someimplementations, the round-trip time (i.e., the amount of time thatelapses while light travels from an active light source of imagingsystem, to a reflector, then back to a light sensor of the system)depends on the depth of the reflector. The better the time resolution ofthe system, the better its depth resolution.

In some implementations of this invention, the system's depth resolutionis so small (and equivalently, its temporal resolution is so fast) thatthe system can resolve a difference in depth that is much less thanλ/(2(NA²), where NA is numerical aperture of the imaging system, and Ais wavelength. In contrast, a conventional camera (with a numericalaperture of NA that does not employ time gating) typically cannot—due tothe diffraction barrier—achieve a depth resolution less than λ/(2(NA²).

For example, in a prototype of this invention, a THz-TDS imaging systememploys time gating, has a numerical aperture of NA≈0.4, and illuminatesthe sample with light of wavelength of 330 microns. In this prototype,at this wavelength, the depth resolution that is actually achieved bytime gating is approximately 150 microns. In contrast, the depthresolution that can be achieved by a conventional camera with the sameNA and same λ, but without time gating, is limited by the diffractionbarrier to a distance equal to λ/(2(NA²)≈2 mm. Thus, in this prototype,due to time gating, the actual depth resolution (about 150 microns) isan order of magnitude smaller than the depth resolution limit (about 2millimeters) that the diffraction barrier typically imposes on aconventional camera with the same numerical aperture. The prototypedescribed in this paragraph is a non-limiting example of this invention.

To summarize this section: In illustrative implementations, time gatingmay enable the imaging system to have ultrafast time resolution. This,in turn, may enable the imaging system to take separate measurements ofreflections arriving from different reflectors at various times.

Staggered Reflectors Beneath Sample

In illustrative implementations of this invention, an imaging systemincludes a set of multiple, small reflectors that are located beneaththe sample being imaged.

For example, in some cases, the reflectors comprise an array ofreflectors (e.g., a 2×2, 3×3, 4×4, or 5×5 array). In some cases, thereflectors comprise a closed-packed (in the x and y dimensions) set ofcircular reflectors. In some other cases, the reflectors comprise atesselated (in the x and y dimensions) set of reflectors.

In illustrative implementations, the reflectors (in the set ofreflectors beneath the sample) are staggered in depth, with eachreflector being at a different depth. For example, in some cases, eachreflector is shifted (in the z dimension) from each of its neighbor(s)by a z-distance of a few hundred microns.

Each reflector (beneath the sample) may have a very small cross-section.For example, in some prototypes of this invention, each reflector iscircular and has a diameter of 220 μm or 440 μm.

In illustrative implementations, the reflectors are good reflectors inthe frequency range of light that illuminates the sample. For example,in some cases, the imaging system includes a THz-TDS spectrometer, andthe reflectors have a high reflectivity for terahertz light. Likewise,in some cases, the imaging system performs OCT with infrared light, andthe reflectors have a high reflectivity in the infrared range. Or, insome cases, the imaging system performs OCT with light in the visualspectrum, and the reflectors are highly reflective in that spectrum.

In some cases, the reflectors may comprise metal, such as copper,aluminum, silver, zinc, or an alloy (e.g., brass) of one or more ofthem. Alternatively, or in addition, the reflectors may in some casesinclude resonant nanostructures to improve reflectivity.

In some cases, each reflector is a flat reflective surface at the top ofan elongated structure. For example, the elongated structure maycomprise a small wire, small pin, or nanopillar.

In some embodiments of this invention, the imaging system is configuredin such a way that, when viewed in a top view, each reflector in the setappears to be partially or entirely inside the beam waist of the lightbeam that illuminates the sample being imaged. Thus, in someembodiments: (a) a set of points in each reflector have the same (x, y)coordinates as those of points in the beam waist; and (b) each reflectoris partially or entirely located (in the x and y dimensions) inside thebeam waist.

FIG. 1A shows a perspective view of a 2×2 array of reflectors, in anillustrative implementation of this invention. In the example shown inFIG. 1A, four reflectors (101, 102, 103, 104) are positioned beneath asample that is being imaged (the sample is not shown in FIG. 1A).

In FIG. 1A, a focused beam of light 121 converges to a circular beamwaist. In FIGS. 1A, 1B, 1D, 1E, 1F: (a) the periphery of the beam waistis circle 130; and (b) the beam waist consists of all points insidecircle 130 that are in the plane of circle 130. At the beam waist, thewidth of the light beam is at a local minimum, because the beam ischanging from converging to diverging at the beam waist. The outersurface of the beam has an inflection point at the beam waist.

In the example shown in FIG. 1A, the four reflectors are located (in thex and y dimensions) entirely inside the beam waist.

In FIG. 1A, the four reflectors (101, 102, 103, 104) are located atgeometric planes 111, 112, 113, 114, respectively. In FIG. 1A, depthincreases from right to left. The four reflectors (101, 102, 103, 104)are staggered in depth: reflector 101 is above reflector 102; reflector102 is above reflector 103; and reflector 103 is above reflector 104.

In FIG. 1A, light wave 132 is emitted by an active light source of theimaging system. Light wave 132 comprises a single pulse (e.g., a pulseof terahertz light emitted by a THz-TDS spectrometer). Light wave 133comprises light that reflects back from the four reflectors, towards thesample and the detector of the spectrometer. Light wave 133 comprisesfour pulses that are reflections from the four reflectors (101, 102,103, 104), respectively. In FIG. 1A, each pulse is shown as a bi-polarpulse to indicate that the single pulse may create a bi-polar pulse inan electrical field in a detector of a THz-TDS spectrometer.

FIGS. 1B-1F each show a top view or side view of reflectors, inillustrative implementations of this invention.

In the examples shown in FIGS. 1A-1J, 2A and 2B, each reflector (e.g.,101, 102, 103, 104, 141, 142, 143, 152, 162, 241, 242, 243, 244, 271,272, 273, 274) is positioned, relative to the imaging system as a wholeand relative to a sample 232, in such a way that light from an activelight source of the system passes through sample 232, then reflects fromthe reflector, then passes through the sample 232 again, and thentravels to a light sensor of the system that directly or indirectlymeasures the light (e.g., by measuring an electric field strength thatis proportional to intensity of incident light). The preceding sentenceis not intended to be a complete list of all interactions of the lightwith elements of the system; in many cases, the light interacts withother optical elements of the system (e.g., lens 234, beam splitter 208,a steering mirror, or any other reflective or transmissive opticalelement of the system). For example, the active light source maycomprise terahertz light source 204, and the light sensor may compriseTHz-TDS detector 206.

FIGS. 1B and 1E each show a top view of a set of reflectors. Thesereflectors are rectangular (e.g., square) in FIG. 1B and are circular inFIG. 1E.

In FIGS. 1B and 1E, each reflector 101, 102, 103, 104 in the 2×2 arrayof reflectors appears—when viewed in top view—to be entirely inside thebeam waist. As noted above, circle 130 is the periphery of the beamwaist. In FIGS. 1B and 1E, the reflectors 101, 102, 103, 104 are located(in the x and y dimensions) entirely inside the beam waist. In FIGS. 1Band 1E, all points in the reflectors 101, 102, 103, 104 have (x, y)coordinates that are the same as those of points in the beam waist.

In FIGS. 1B-1F, the diameter of the beam waist is distance w₆.

FIG. 1C shows a side view of the reflectors shown in FIG. 1A. In FIG.1C, the optical axis 131 intersects a sample 232. Reflectors 101, 102,103, 104 are located beneath the sample.

In FIG. 1C: (a) if light were to travel along optical axis 131 from theright to the left side of FIG. 1C, then the light would be movingoptically away from an active light source (e.g., 204) that illuminatesthe sample; and (b) if light were to travel along optical axis 131 fromthe left to the right side of FIG. 1C, then the light would be movingoptically toward a light sensor (e.g., THz-TDS detector 206) of theimaging system.

As used herein, to say that two reflectors are “z-neighbors” or are“z-neighboring” means that they are neighbors in the z-dimension. Forexample, in FIG. 1C, reflector 104 has only one z-neighbor:specifically, reflector 103. Reflector 103 has only two z-neighbors:specifically, reflectors 104 and 102. Reflector 102 has only twoz-neighbors: specifically, reflectors 103 and 101. Reflector 101 hasonly one z-neighbor that is a reflector: specifically, reflector 102.

In FIG. 1C, the z-distance between reflectors 101 and 102 is distancea₁. The z-distance between reflectors 102 and 103 is distance a₂. Thez-distance between reflectors 103 and 104 is distance a₃.

In FIG. 1C, the sum of the z-distances between z-neighbors is a₄; thatis a₄=a₁+a₂+a₃.

In many cases, the reflectors are flat and specular.

However, each reflector diffracts light when it reflects light. In manycases, a reflector is sufficiently small that the effects of thisdiffraction are significant, causing the light that reflects from thereflector to diverge significantly.

In illustrative implementations, it is desirable to prevent light (thatdiffracts when it reflects from a reflector) from diverging too far (inthe x and y dimensions). To prevent this, in some cases, the sum of thez-distances (e.g., sum a₄) between z-neighboring reflectors is less thand/(2 tan(Ø)), where d is the diameter w₆ of the beam waist, and where Øis the divergence angle of light that reflects (and thus diffracts) fromthe lowest reflector. In FIG. 1C, distance a₅ is equal to d/(2 tan(Ø)).

In many cases, the distance between the sample and the reflector that isfarthest away from the sample is much less than λ/(2(NA²), where NA isnumerical aperture of the imaging system, and A is wavelength. (As notedabove, λ/(2(NA²) is a limit on the depth resolution that can betypically be achieved by a conventional camera without time gating). Forexample, in FIG. 1C, distance a₆ is the distance between sample 232 andreflector 104 (the reflector which is farthest from the sample). In theexample shown in FIG. 1C, distance a₆ is much less than λ/(2(NA²).

As noted above, in illustrative implementations, light reflecting fromdifferent reflectors arrives at a light sensor (e.g., a detector of aTHz-TD spectrometer) at different times. In many cases, this differencein time-of-arrival is because: (a) the reflectors are staggered indepth, each reflector being at a different depth; and thus (b) theround-trip distance is different for each reflector. As used herein,“round-trip” distance for a reflector means the total distance thatlight travels, in a path from the active light source of the system tothe reflector and then to a light sensor of the system.

In illustrative implementations, the imaging system produces asuper-resolved image of a sample, by extracting x, y spatial informationfrom time-resolved data regarding reflected light that reaches thesensor at different times due to different depths of the reflectors.

Thus, in illustrative implementations, it is desirable for the system tobe able to temporally resolve light that reflects from differentreflectors and arrives at the imaging sensor at different times.

In many cases, the z-distance between each pair of z-neighboringreflectors, respectively, is greater than half the coherence length oflight illuminating the sample. For example, in FIG. 1C: (a) distance a₀is equal to the half the coherence length; and (b) distances a₁, a₂, anda₃ are each greater than distance a₀.

Furthermore, in many cases, in order to achieve this time resolution,the z-distance between each pair of z-neighboring reflectors,respectively, is greater than the system's time resolution distance. Forexample, in FIG. 1C, z-distances a₁, a₂, and a₃ are each greater thanthe system's time resolution distance. As used herein, “time resolutiondistance” of an imaging system means the distance that light travelsduring a period of time, which period is equal to the smallest intervalof time for which the system can temporally resolve between two pulsesof light.

In many implementations, the reflectors (e.g., 101, 102, 103, 104)beneath the sample all have the same size, shape, albedo and otherreflective properties.

Alternatively, in some cases, one or more of these factors (size, shape,albedo or other reflective property) is not the same for all of thereflectors beneath the sample. For example, in some cases, one or moreof these factors (size, shape, albedo or other reflective property) isvaried in such a way that the relative intensity of light reflected froma given reflector is increased. For example, in some cases, it may bedesirable to increase the relative intensity of light reflected byreflectors that are at a greater distance from the sample. Likewise, insome cases, if there are a large number of reflectors in the array, itmay be desirable to increase the relative intensity of light reflectedby reflectors that are located (in the x and y dimensions) closer to theperiphery of the array. For example, the relative intensity of lightthat reflects from a given reflector may be increased by increasing itsrelative size, or by increasing its relative albedo. In this paragraph:(a) “relative” means relative to other reflectors in the array; and (b)thus, for example, relative albedo of a given reflector means the albedoof the given reflector, relative to the albedo of the other reflectorsin the array.

FIGS. 1D and 1F each show a top view of a set of reflectors. Thesereflectors are rectangular (e.g., square) in FIG. 1D and are circular inFIG. 1F.

In FIGS. 1D and 1F, each reflector in the set of reflectors (e.g., 101,102, 103 and 104, or 141, 142, 143) appears—when viewed in top view—tobe only partially inside the beam waist. As noted above, circle 130 isthe periphery of the beam waist. Thus, in FIGS. 1D and 1F, eachreflector 101, 102, 103, 104, 141, 142, 143 is located (in the x and ydimensions) only partially inside the beam waist. In FIGS. 1D and 1F,only a subset of points in each reflector 101, 102, 103, 104, 141, 142,143 have (x, y) coordinates that are the same as those of points in thebeam waist.

FIGS. 1G and 1I each show a reflector that comprises a flat end of anelongated structure, in illustrative implementations of this invention.The elongated structure (161, 151) has a rectangular cross-section inFIG. 1G and a circular cross-section in FIG. 1I.

In the examples shown in FIGS. 1G and 1I: (a) a reflector 152, 162comprises a flat, specular, reflective surface; (b) the elongatedstructure 151, 161 has a longitudinal axis 154, 164; (c) the reflector152, 162 is located at a longitudinal end of the elongated structure151, 152; and (d) the elongated structure 151, 161 has an aspect ratioof 1:x, where x is a finite number greater than or equal to 2.

FIGS. 1H and 1J show cross-sectional views of the elongated structuresin Figures IG and 1I, respectively. The cross-section for FIGS. 1H and1J is taken in a cross-sectional plane 153, 163 which: (a) isperpendicular to the longitudinal axis 154, 164 of the structure 151,161; and (b) is coplanar with the flat surface of the reflector 152,162.

This invention is not limited to square, rectangular or circularreflectors. In illustrative implementations, a reflector may have any 2Dor 3D shape, and may comprise a surface on a structure that has anycross-sectional shape.

In many implementations, the set of reflectors beneath the sample (andeach reflector in the set) are small relative to the diameter of beamwaist and relative to the wavelength of light illuminating the sample.

In many cases, this small size is desirable, to ensure that the set ofreflectors (which are staggered in depth and thus reflect light atdifferent times) occupy a sufficiently small region that the reflectedlight from the reflectors encodes (in time) data from which asuper-resolved image of the sample may be extracted.

The following discussion gives examples of small sizes, in someimplementations of this invention. However, before discussing thesenon-limiting examples of small size, it is helpful to first define“maximum dimension” and “convex hull”.

As used herein, the “maximum dimension” of an object means the longestdistance between any two points of the object. For example, the maximumdimension of a circle is the diameter of the circle. Also, for example,if the sides of a square each have length A, then the maximum dimensionof the square is √{square root over (2)}A (the length of the diagonalbetween two opposite vertices of the square).

As used herein, the term “convex hull” is used in its mathematicalsense. For example, a convex hull of a set Q of points in a Euclideanplane is the smallest convex set that contains Q. Also, for example, inFIG. 1C, the region enclosed by line 133 is the convex hull of the fourrectangles 101, 102, 103, 104.

Now that we have these definitions, we list some non-limiting examplesof small sizes of the set of reflectors (or of each reflector).

In some cases, the maximum dimension (e.g., w₄ in FIG. 1C) of the convexhull of the set of the reflectors is less than the diameter of the beamwaist.

In some cases, the maximum dimension (e.g., w₄ in FIG. 1C) of the convexhull of the set of the reflectors is less than the wavelength of themaximum intensity frequency component of light illuminating the sample.

In some cases: (a) the set of reflectors comprises a “rectangular grid”array of reflectors; and (b) the length of the longest straight linesegment along any side of the array (e.g., w₂ in FIG. 1C) is less thanthe diameter of the beam waist.

In some cases: (a) the set of reflectors comprises a “rectangular grid”array of reflectors; and (b) the length of the longest straight linesegment along any side of the array (e.g., w₂ in FIG. 1C) is less thanthe wavelength of the maximum intensity frequency component of lightilluminating the sample.

In some cases, the maximum dimension (e.g., w₃ in FIG. 1C) of eachreflector in the set, respectively, is less than 1/R times the diameterof the beam waist, where R is any number greater than or equal to 1.5.

In some cases, the maximum dimension (e.g., w₃ in FIG. 1C) of eachreflector in the set, respectively, is less than 1/R times thewavelength of the maximum intensity frequency component of lightilluminating the sample, where R is any number greater than or equal to1.5.

In some cases: (a) each reflector in the set is a polygon; and (b) thelength of the longest straight line segment of a side of the polygon(e.g., w₁ in FIG. 1C) is less than 1/R times the diameter of the beamwaist, where R is any number greater than or equal to 1.5.

In some cases: (a) each reflector in the set is a polygon; and (b) thelength of the longest straight line segment of a side of the polygon(e.g., w₁ in FIG. 1C) is less than 1/R times the wavelength of themaximum intensity frequency component of light illuminating the sample,where R is any number greater than or equal to 1.5.

For purposes of the preceding four paragraphs, non-limiting examples ofvalues of R include 1.5, 2, 2.154, 3, 4, and 5. In some cases, whichvalue of R is desirable for a given implementation of this invention maydepend on factors such as the number of reflectors or positioning of thereflectors relative to each other in the x and y dimensions (e.g.,array, tessellation, or close-packed). For example, selecting R=2.154may be appropriate in a case in which the set of reflectors consists ofthree closed-packed circles (because the smallest circle that enclosesthree close-packed circles has a radius that is about 2.154 times theradius of each of the close-packed circles).

For purposes of preceding nine paragraphs: (a) the z-dimension isignored; (b) each shape is treated as being a 2D shape that exists onlyin the x and y dimensions; that is, each given shape is treated as beingthe orthogonal projection of that given shape onto the x-y plane; and(c) all distances are measured in the x and y dimensions only. Forexample, if the (x,y,z) coordinates of a first point, second point andthird point were (0,0,0), (0,1,2), and (1,0,18) respectively, then, forpurposes of the preceding nine paragraphs: (a) the first, second andthird points would be treated as points in 2D space with (x,y)coordinates of (0,0), (0,1) and (1,0), respectively; and (b) thedistance between the first and third points would be treated as 1 (not√{square root over (1²+18²)}).

This invention is not limited to any particular number of reflectors.For example, the set of reflectors beneath the sample may consist of:(a) three reflectors (e.g., three close-packed circular reflectors); (b)four reflectors (e.g., a 2×2 array of reflectors); (c) seven reflectors(e.g., seven circular reflectors that are close-packed so that sixreflectors are arranged in a circle around a central reflector); (d)nine reflectors (e.g., in a 3×3 array); (e) sixteen reflectors (e.g., ina 4×4 array); (f) twenty-five reflectors (e.g., in a 5×5 array); or (g)any other number of reflectors.

As noted above, in many cases, the imaging system produces asuper-resolved image of a sample, by extracting x, y spatial informationfrom time-resolved data regarding reflected light that reaches thesensor at different times due to different depths of the reflectors.

In illustrative implementations, increasing the number of reflectors (inthe set of reflectors beneath the sample) tends to increase the x, yspatial resolution of the super-resolved image. However, increasing thenumber of reflectors may tend to increase the SNR (signal-to-noiseratio) of the system, because (all other factors being equal) thesmaller the area of a reflector, the less light that will be reflectedback from the reflector.

As noted above, in some cases: (a) light that reflects from eachreflector diverges (e.g., due to diffraction) at a divergence angle; and(b) the sum of z-distances between z-neighboring reflectors may be lessthan d/(2 tan(Ø)), where d=w₆ is the diameter of the beam waist and Ø isthe divergence angle.

In some cases, the reflectors are engineered to decrease the divergenceangle. For example, the divergence angle of light reflecting from areflector may be reduced by: (a) etching the top surface of thereflector with sub-wavelength periodic metallic structures in such asway to create destructive interference at larger angles; (b) fabricatingnano-antenna or micro-antenna arrays at the top of the reflector; (c)fabricating a parabolic surface at the top of the reflector; or (d)applying one or more thin layer coatings in such way as to createdestructive interference at larger angles.

Decreasing the divergence angle may be desirable, at least in somecases. For example, decreasing the divergence angle may, in turn, allowthe sum of the z-distances (between z-neighboring reflectors) to beincreased. Increasing the sum of z-distances may, in turn, facilitateincreasing the number of reflectors, while keeping the distance of eachz-step constant. Or, increasing the sum of the z-distances may bedesirable, in order to increase distance of each z-step, which in turnmay facilitate employing a time-of-flight sensor that has a slowertemporal resolution. With a smaller reflection angle from eachreflector, the distance from the entire array and the sample may also befurther increased.

THz-TDS Imaging with Staggered Reflectors Beneath Sample

FIG. 2A shows hardware for a THz-TDS imaging system that includesreflectors at staggered depths beneath the sample, in an illustrativeimplementation of this invention. In the example shown in FIG. 2A, aTHz-TDS spectrometer 283 comprises a terahertz light source 204, a beamsplitter 208 and a detector 206. Detector 206 may measure incident lightby measuring an electric field.

In FIG. 2A, terahertz light source 204 emits ultrashort pulses ofterahertz light. Each pulse of terahertz light is emitted by lightsource 204, then reflected by beam splitter 208, then focused byobjective lens 234, then travels through a sample 232, and then isreflected by reflectors 241, 242, 243, 244. Because the four reflectors241, 242, 243, 244 are at different depths, each pulse of light emittedby light source 204 is reflected back (from the reflectors) as a timesequence of four fainter pulses. These four fainter pulses of reflectedlight travel through sample 232 again, then are transmitted by beamsplitter 208, and then travel to, and are measured by, detector 206 ofthe THz-TDS system. Thus, in FIG. 2A, the impulse response of the fourreflectors to a single pulse of terahertz limit emitted by light source204 is a time sequence of four fainter pulses that reflect back from thereflectors toward the sample and the THZ-TDS detector.

In addition, some light reflects directly back from sample 232 todetector 206, without ever reaching the reflectors. In illustrativeimplementations, this light that reflects directly back from the sample(without reaching the reflectors) is not used when generating thesuper-resolved image of the image.

In FIG. 2A, the reflectors 241, 242, 243, 244 are beneath the sample 232and are staggered in depth, with each reflector being at a differentdepth. Furthermore, the reflectors are very small and fit closelytogether.

In FIG. 2A, objective lens 234 refracts light (from light source 204) insuch a way that it forms a beam of light that converges to a focus in asmall 3D region of focus that includes reflectors 241, 242, 243, 244 anda portion of sample 232 located above the reflectors. In a plane that isparallel to the x-y plane, the smallest cross-section of this region offocus is a circular focal spot. (In the example shown in FIGS. 1A, 1B,1D, 1E, 1F, circle 130 is the periphery of the circular focal spot andis also the periphery of the beam waist).

In FIG. 2A, reflectors 241, 242, 243, 244 are located (in the x and ydimensions) entirely within the circular focal spot. Alternatively, inFIG. 2A, reflectors 241, 242, 243, 244 are each located (in the x and ydimensions) only partially within the circular focal spot.

In FIG. 2A, distance a₆ is the distance between sample 232 and reflector242 (the reflector which is farthest from the sample). In the exampleshown in FIG. 2A, distance a₆ is much less than λ/(2(NA²).

In FIG. 2A, the sample is much larger than the circular focal spot. Inorder to capture an image of the entire sample, the sample may berastered in the x and y dimensions, thus causing the circular focal spotof light to be positioned at different x, y positions of the sample atdifferent times. An actuated stage includes stage 221 and actuator 223.Stage 221 supports sample 232. Actuator 223 may actuate x and y motionof stage 221 and thus sample 232. Actuator 223 may comprise one or moremotors. In FIG. 2A, objective lens 234 and reflectors 241, 242, 243, 244may remain stationary, relative to the imaging system as a whole, whilethe sample is rastered in the x and y dimensions.

Alternatively, in some cases, rastering is not performed. For example,in some cases: (a) the sample is smaller than the array of reflectorsand is located (in the x and y dimensions) entirely within the circularfocal spot; and (b) thus, rastering is avoided. Or, in some cases, anarray of detectors may be employed, each focused at a different circularfocal spot, and the sample and its stage may remain stationary (insteadof being rastered).

In FIGS. 2A and 9, stage 221, 921 may support sample 232, 932 directly,or may indirectly support the sample by supporting a transparent object(e.g., a slide) to which the sample 232, 932 is attached. For example,in some cases: (a) sample 232, 932 is attached to a transparent slide;stage 221, 921 includes a circular hole; (b) the sample and slide may bepositioned in such a way that a portion of the sample is above thecircular hole, allowing light to pass through the circular hole, slideand sample; (c) edges of the slide may extend beyond the circular holeand be supported by the stage; and (d) the stage may include arms, clipsor other devices that hold the slide in position while the sample isbeing imaged.

In FIG. 2A, a computer 230 may control and interface withmicrocontrollers 292, 294, 296, which in turn may control and interfacewith light source 204, light sensor 206, and actuator 223, respectively.The computer 230 may output instructions that cause the light source,light sensor and actuated stage to operate in a synchronized manner. Forexample, the computer 230 may output instructions that cause theactuated stage to raster the sample to a new x, y position, and thencause the light source to emit a light pulse and the light sensor tocapture an image, while the sample is in this new x, y position.Computer 230 may store data in, and access data from, memory device 290.In FIG. 2A, devices in the imaging system may communicate with eachother via a set of wires (e.g., 281, 282, 283). Alternatively, in somecases, devices in the imaging system may employ wireless modules (e.g.,291, 293, 295) to communicate with each other by wireless communication.

In FIG. 2A, sample 232 is translucent, in the frequency range of lightthat illuminates the sample. For example, in some cases, sample 232 istranslucent to, and illuminated by, terahertz light. Preferably, sample232 is thin in the z-dimension (e.g., has a thickness less than tentimes the wavelength of light illuminating the sample). This tends toreduce interreflections within the sample and to increase transmissionof light through the sample.

In FIGS. 2A and 2B, reflectors 241, 242, 243, 244, 271, 272, 273, 274comprise flat reflective surfaces at the longitudinal ends of elongatedstructures 211, 212, 213, 214, 261, 262, 263, 264, respectively.Elongated structures 211, 212, 213, 214, 261, 262, 263, 264 may, forexample, comprise wires, pins or nanopillars, and may, in some cases, becovered with resonant structures to increase reflectivity.

In some cases, the flat reflective surface of the reflectors is producedby ablation of a tip of an elongated structure, or by physically cuttingan elongated structure into two parts.

In some cases, it is desirable for the elongated structures (and thusreflectors) to have a square or rectangular cross-section. This isbecause a square or rectangular cross-section facilitates a high packingdensity of reflectors in a “grid” array. However, in many cases, it iseasier to fabricate elongated structures (and thus reflectors) that havea circular cross-section. The elongated structures (and the reflectors)have a square cross-section in FIG. 2A and a circular cross-section inFIG. 2B.

This invention is not limited to the hardware shown in FIG. 2A. Any typeof THz-TDS spectrometer may be employed, in illustrative implementationsof this invention. For example, in some cases, the THz-TDS spectrometeroperates in transmission mode or detection mode, and detects returningterahertz radiation by photoconductive antennas or nonlinear crystals.

In illustrative implementations of this invention, the THz-TDSspectrometer may generate terahertz radiation in a variety of differentways. For example, a photoconductive emitter (sometimes calledphotoconductive switch) may emit pulsed terahertz radiation. Thephotoconductive emitter may include a laser (e.g., a mode-locked fiberlaser, or a Ti-Sapphire laser) and biased antenna electrodes patternedin a semi-conductor material. The laser may emit an ultrashort laserpulse that causes a sudden electric current to flow across theseelectrodes, which in turn causes a pulse of terahertz radiation to beemitted. Or, for example, the THz-TDS spectrometer may employ opticalrectification. In the optical rectification, an ultrashort laser pulse(e.g., emitted by an amplified Ti-Sapphire laser) may pass through atransparent crystal, causing a pulse of terahertz radiation to beemitted.

In illustrative implementations of this invention, the THz-TDSspectrometer may detect a pulse of incident terahertz light (that isreturning from the sample being imaged). For example, a detection pulse(which is a portion of the laser pulse that triggered the terahertzradiation) may be steered into a detector. In the detector, the electricfield of the terahertz pulse (that reflects from the scene) may interactwith the much shorter detection pulse, producing an electrical signalthat is proportional to the electric field of the terahertz pulse. Byrepeating this process (and by using an optical delay line to vary thetiming of the detection pulse in different repetitions), differentfrequencies in the terahertz pulse may be scanned and the electric fieldof the terahertz pulse as a function of time may be determined. Then aFourier transform may be performed on this time-domain signal, tocalculate a frequency spectrum.

In illustrative implementations of this invention, the THZ-TDSspectrometer may detect the terahertz radiation (that returns from thesample being imaged) in a variety of different ways. For example,antennas used in photoconductive generation of the terahertz radiationmay be employed to detect the returning terahertz radiation, byphotoconductive detection. In this approach, the returning terahertzradiation may drive electric current across the antenna leads, and anamplifier may amplify this current. The amplified current may correspondto the field strength of the returning terahertz radiation. Or, forexample, the crystals used for optical rectification generation of theterahertz radiation may be employed for detecting the returningterahertz radiation. The crystals may be birefringent in an electricfield, causing a change in polarization of the terahertz radiation thatis proportional to the electric field strength. This change inpolarization may be measured.

In some implementations: the detector (e.g. 206) of the THz-TDSspectrometer measures incident terahertz light by measuring an electricfield, and thus the detector (e.g., 206) is an example of a lightsensor. Other types of light sensors may be employed in this invention.

In illustrative implementations, either terahertz time-domainspectroscopy (THz-TDS) or optical coherence tomography (OCT) may beemployed. An advantage of employing a THz-TDS spectrometer is that thedetection process in THz-TDS may be based on electric field measurementswith ultrafast (e.g., femtosecond) time steps, which are more directlyaccessible measurements than autocorrelation which may be used in OCT.

The following six paragraphs describe a prototype of this invention.

In this prototype, a THz time domain spectrometer includes afiber-coupled laser and photoconductive switches. An objective lenscomprises an HDPE (high-density polyethylene) lens with 5 cm focallength. This lens focuses THz light from the spectrometer onto a 2×2array of reflectors, creating a focal spot between 500 um and 1 mm indiameter.

In this prototype, the reflectors are packed closely together, and havea diameter of 220 μm each (or 440 μm each). The reflectors are copper orbrass wires with polished tips to reflect the THz light back.

In this prototype, the reflectors are positioned at different depths,and thus reflect a pulse of light at different times relative to eachother. These time-gated reflections enable time-encoding of informationfrom which super-resolved image may be extracted.

In this prototype, the sample has thickness (300 μm) that is comparableto the wavelength of the incident light.

In this prototype, the emitted THz light is focused on to the samplewith a high-density-polyethylene HDPE lens of numerical aperture NA,diameter D, focal length f, and imaging medium refractive index of n,where (NA=nD/2f=1×25/2×30≈0.4). In this prototype, the reflectors are atthe ends of pins in a 2×2 metallic pin array.

In this prototype, the diameter of each reflector is 220 μm or 440 μmdiameters, and each reflector is shifted in z by a few hundred micronsrelative to its neighbor(s) in the z dimension.

The prototype described in the preceding six paragraphs is anon-limiting example. This invention may be implemented in many otherways.

FIGS. 3A, 3B, 3C, 4A, 4B, 4C, 4D, 4E are images of reflected light, inillustrative implementations of this invention.

FIGS. 3A and 3B show light reflecting from four reflectors at anarbitrary x, y point. In FIGS. 3A and 3B, the arbitrary x, y point isx=2.5 mm and y=2.4 mm. (The vertical dashed lines in FIGS. 3A and 3B areat x=2.5 mm and y=2.4 mm, respectively.)

FIGS. 3A and 3B are x-z and y-z images, respectively. Thus, in FIGS. 3Aand 3B, the vertical axis is the z dimension. Different coordinatesalong the z axis of FIGS. 3A and 3B correspond to different depths ofthe reflectors. Different coordinates along the z-axis in FIGS. 3A and3B also correspond to different times-of-arrival (at the THZ-TDSdetector) of light that reflected from the reflectors. This is becausethe round-trip distance that light travels to and from a givenreflector—and the amount of time it takes for light to traverse theround-trip distance—is different depending on the depth of the givenreflector. Thus: (a) in FIGS. 3A and 3B, the vertical axis is equivalentto time-of-arrival of light; and (b) the x-z and y-z images areequivalent to x-t and y-t images, respectively. (In an x-t or y-t image,the vertical axis is time.)

In FIGS. 3A and 3B, the image shows four bi-polar pulses of electricfield strength measured by a THz-TDS spectrometer. These four bi-polarpulses arrive at the detector of the THz-TDS spectrometer at differenttimes, each from a different reflector at a different depth. Thus, thesefour pulses are shown in different positions on the z-axis, becausedifferent positions on the z-axis correspond to different depths of thereflectors and thus to different times-of-arrival of light. In FIGS. 3Aand 3B, the first, second, third and fourth bi-polar pulses are located(in the z-dimension) at approximately 2.4-2.5 mm, 2.0-2.1 mm, 1.4-1.5mm, and 0.8-0.9 mm, respectively.

In the example shown in FIGS. 3A and 3B, each bi-polar pulse is smearedin the horizontal (x or y dimension) and is not smeared in the vertical(depth or time) dimension. This is because light may diffract (and thusdiverge) when it reflects from the reflectors. Thus, a diverging beam oflight may reflect from each reflector, and the divergence (in the x andy dimensions) may cause the smearing in the horizontal dimension of x-zand y-z images shown in FIGS. 3A and 3B. In many implementations, thereflectors themselves do not overlap in the x and y dimensions, eventhough diverging reflections of light from the reflectors overlap in (inthe x or y dimension) in images captured by a THz-TDS spectrometer.

In FIGS. 3A and 3B, the four bi-polar pulses of light are the impulseresponse of the four reflectors to a single pulse of terahertz lightemitted by a THz-TDS spectrometer. This single pulse travels from thespectrometer, through the sample, and to the respective reflectors,which reflect it back as four separate pulses due to the differentdepths of the reflectors (a separate pulse for each reflector). Thesefour reflected pulses then travel pass through the sample and travel tothe spectrometer.

In some implementations: (a), a thin sample is inserted above thereflectors; and (b) the direct reflection from the sample itself isstronger than the signal from the reflectors. Although this reflectionfrom the sample is separable in time, it notably reduces the signal thatreaches the reflectors and comes back to the light sensor of the system(e.g., a detector of a THz-TDS spectrometer).

FIG. 3C shows a x-t image of light that reflected from a sample and fromfour reflectors. In FIG. 3C, the vertical axis is time (specifically,time of arrival of light at the detector of a THz-TDS spectrometer).

In FIG. 3C, a bi-polar pulse of light that reflected directly from thesample is recorded as two prominent horizontal smears in vertical region300 of the image. In FIG. 3C, four fainter bi-polar pulses alsoreflected from the four reflectors, respectively. In FIG. 3C, these fourpulses are centered (in the time dimension) at dashed lines 301, 302,303, 304, respectively. In FIG. 3C, each bi-polar pulse from a reflectorappears as a pair of faint horizontal smears.

In FIG. 3C, the five bi-polar pulses of light (one from the sample andfour from the four reflectors) are the impulse response of the sampleand four reflectors to a single pulse of terahertz light emitted by aTHz-TDS spectrometer. The five pulses (reflected from the sample andfour reflectors, respectively) arrive at a detector of the THz-TDSspectrometer at different times, because of the different depths of thereflectors.

In illustrative implementations, the light sensor (e.g., a detector of aTHz-TDS spectrometer) captures information about incident radiation ateach x, y pixel at different times. Thus, the light sensor may capturedata that comprises an x-y-t data cube. For example, FIGS. 3A, 3B and 3Crepresent planar “slices” of an x-y-t data cube (or, equivalently, x-y-zdata cube). In FIG. 3A, the slice is an x-z (or equivalently, x-t)plane. In FIG. 3B, the slice is a y-z (or equivalently, y-t) plane. InFIG. 3C, the slice is an x-t (or equivalently, x-z) plane.

FIG. 3D shows an HSV (hue, saturation, value) color map that is employedin FIGS. 3A, 3B and 3C. The normalized electric field strength(normalized to the value of the positive peak of the bipolar THzelectric field pulse) measured by the THz-TDS spectrometer may rangebetween −1 and +1. Different colors in this HSV color map correspond todifferent values of the normalized electric field strength.Specifically: (a) the higher (vertically) a given color is in the HSVcolor map shown in FIG. 3D, the closer the electric field strength thatthe given color represents is to +1; and (b) the lower (vertically) aspecific color is in the HSV color map shown in FIG. 3D, the closer theelectric field strength that the specific color represents is to −1.Thus, in this HSV color map, dark blue represents a positive electricfield strength.

FIGS. 4A, 4B, 4C, and 4D are x-y images of light reflecting from a firstreflector, second reflector, third reflector and fourth reflector,respectively. Each of these images were taken at different times.Specifically, FIGS. 4A, 4B, 4C, and 4D were captured when light from thefirst, second, third and fourth reflectors, respectively, reached theTHz-TDS detector. In the example shown in FIGS. 4A-4D, thesetimes-of-arrival are different, because the reflectors are at differentdepths, and thus the amount of time that light takes to travel from theTHz-TDS spectrometer to the reflector and back to the spectrometer) isdifferent for each reflector. In each of these four images (FIGS.4A-4D), the star * marks the peak (in the x and y dimensions) ofintensity of the reflection and thus indicates the location (in the xand y dimensions) of the center of the reflector.

FIG. 4E is an x-y-z image (or equivalently x-y-t image) of lightreflecting from four reflectors. In FIG. 4E, the vertical dimension isthe z-dimension. Different positions along the vertical axis correspondto different depths of reflectors (or, equivalently, differenttimes-of-arrival of light from the reflectors). FIGS. 4A, 4B, 4C and 4Dare x-y planar slices of the x-y-z image in FIG. 4E. These x-y sliceswere taken at different times-of-arrival at the THz-TDS detector.

In FIGS. 4A, 4B, 4C, 4D, 4E, the light that is recorded is the impulseresponse of the reflectors to a single pulse of terahertz light emittedby a THz-TDS spectrometer. This single pulse travels from thespectrometer, through the sample, and to the respective reflectors,which reflect it back as separate pulses due to the different depths ofthe reflectors (a separate pulse for each reflector). These separatereflected pulses then pass through the sample and travel back to thespectrometer.

In some implementations, window functions are used to separate data foreach reflector.

FIG. 4F is a JET color map that is employed in FIGS. 4A, 4B, 4C, 4D and4E. Different colors in this JET color map correspond to differentvalues of normalized intensity. Specifically, the higher (vertically) acolor is in the JET color map shown in FIG. 4F, the greater theintensity of incident light.

FIGS. 5A and 5B are charts of measurements taken by a single pixel of aTHz-TDS spectrometer, in an illustrative implementation of thisinvention.

FIG. 5A is a chart of normalized electric field strength vs. time, formeasurements taken by a single pixel of a THz-TDS detector. (Recall thata THz-TDS detector measures an electric field strength that isproportional to intensity of light).

In FIG. 5A, solid line 503 represents measurements taken when a 2×2array of four reflectors are beneath the sample. The dominant peak 520of signal 503 records a pulse of light that reflected directly back fromthe sample. Four smaller peaks or troughs (specifically, a trough, thena peak, then a trough, then a peak) of signal 503 occur later duringtime intervals 510, 512, 514, 516, respectively. These smaller peaks ortroughs of signal 503 correspond to fainter pulses of light that returnfrom the first, second, third and fourth reflectors, respectively.

In FIG. 5A, dotted line 501 represents measurements taken when noreflectors are beneath the sample. Again, the dominant peak 520 ofsignal 501 records a pulse of light that reflected directly back fromthe sample. Small peaks and troughs occur later in signal 501,corresponding to interreflections that occur in the sample itself.

FIG. 5B is a chart of normalized electric field strength vs. time, formeasurements taken by a single pixel of a THz-TDS detector. FIG. 5Bshows four separate signals 541, 542, 543, 544 caused by reflectionsfrom four reflectors, respectively. These four signals are separated intime (except for a short period of overlap at the beginning or end ofthe signals).

In FIGS. 5A and 5B, the electric field strength is normalized to thepositive peak, not the entire range.

FIGS. 6A-6G are images captured by a THz-TDS spectrometer, in anillustrative implementation of this invention.

FIG. 6A is an image formed by THz light that reflected directly from asample, and did not pass through the sample to the reflectors beneath.This direct reflection produces the dominant peak of the reflected lightsignal returning to the detector of the THz-TDS spectrometer (seedominant peak 520 in FIG. 5A). In FIG. 6A, this sample comprises paperwith hexagonal metallic patterns that contains the letters “T O P P aN”. In FIG. 6A: (a) the SNR (signal-to-noise ratio) of the image is highbecause the metal in the sample is very reflective in the terahertzrange of frequencies; (b) because the SNR is high, the image is clear;and (c) however the resolution (50×50) in FIG. 6A is lower than theresolution in the super-resolved image (100×100) in FIG. 6G, because thedata in FIG. 6A is from the dominant peak.

FIG. 6B is an image formed by THz light that reflected internally withinthe sample, before traveling back to the detector of the THz-TDSdetector. This shows that, even though the sample was very thin, someinterreflections inside the sample occurred.

FIGS. 6C-6F are images formed by THz light that was emitted by a THz-TDSspectrometer, then passed through the sample, then reflected from areflector, and then passed through the sample again. In FIGS. 6C, 6D,6E, 6F, the light that reflected from a first, second, third and fourthreflector, respectively. FIGS. 6C, 6D, 6E, 6F were each captured duringa different interval of time, corresponding to when light reached theTHz-TDS detector from the first, second, third and fourth reflector,respectively.

FIG. 6G is a super-resolved image, with a 100×100 spatial resolution inthe x and y dimensions. Thus, the minimum resolvable x, y distance inFIG. 6G is reduced by a factor of 2 (as compared to the image in FIG.6A), and the amount of information in FIG. 6G is four times greater thanin FIG. 6A. However, in FIGS. 6A-6G, metallic material in the samplemakes the sample very reflective in the terahertz range of frequencies.Thus, the SNR of the images in FIGS. 6C-6F (which record or are derivedfrom data regarding fainter reflections from the reflectors) is an orderof magnitude lower than the SNR of the image in FIG. 6A (which recordsthe brighter direct reflection from the sample). This low SNR reducesthe clarity of the image in FIG. 6G. However, much better clarity in thesuper-resolved image may be achieved by choosing other materials for thesample.

To generate FIGS. 6A-6F: (a) time-domain signals were measured by aTHz-TDS detector; and (b) each of these time-domain signals weremultiplied by a window function, then transformed by an FFT (fastFourier transform), and then integrated over a 1.2 THz to 2.3 THz rangeof frequencies in the Fourier domain.

In some implementations, the reflectors are staggered in depth beneaththe sample, in such a way that pulses of light reflecting back from thereflectors arrive at a THz-TDS detector sensor during a different timeinterval for each reflector. The detector may temporally resolve—thatis, measure separately during different time intervals—the terahertzpulses that arrive at different times from different reflectors. Thedetector may thus acquire a set of separate measurements, each of which,respectively, measures a terahertz pulse of light that reflected from aparticular reflector during a particular time interval. One or morecomputers may then combine these separate measurements to create aspatially super-resolved image.

In this super-resolved image, there may be a spatially resolved,separately measured light intensity for the tiny x-y region of thesample that is directly above each reflector, respectively—even thoughthe tiny x-y regions that correspond to the reflectors may be so smallthat the diffraction barrier would ordinarily prevent them from beingspatially resolved. This is because the THz-TDS detector may take aseparate measurement for each reflector (and its corresponding tiny x-yarea of the sample), respectively. This ability to measure light fromeach reflector (and its corresponding tiny x-y region of the sample)separately may arise because: (a) for each reflector, light thatreflects from the reflector passes though a corresponding tiny x-yregion of the sample (while traveling to and from the reflector); (b)the reflectors are staggered in depth in such at way that light fromeach reflector (and its corresponding x-y region of the sample), reachesthe THz-TDS detector during a different time interval; and (c) the lightsensor takes a separate measurement during each of these different timeintervals. Thus, there may be a separate measurement of light thatreflects from each reflector (and its corresponding x-y area of thesample), respectively. Then the separate measurements taken at theseparate times may be computationally combined to generate a spatiallysuper-resolved image.

As noted above, the separate measurements for each reflector may beacquired by separating data in post-processing.

FIGS. 7, 8, 10 and 11 are flow-charts of imaging methods, inillustrative implementations of this invention.

FIG. 7 is a flow-chart of a method for THz-TDS imaging which employs aset of reflectors that are staggered in depth beneath a sample. In theexample shown in FIG. 7, the method includes the following steps: Aterahertz pulse is generated using a THz-TDS system (Step 701). Thepulse is focused on the reflector array beneath the 2D sample. In thepreceding sentence, to say that a sample is “2D” means that thethickness of the sample is less than ten times the wavelength of lightilluminating the sample (Step 702). The sample is raster scanned usingan automated stage (Step 703). Measured data cube is processed in timedomain or frequency domain to create a super-resolved image (Step 704).

FIG. 8 is a flow-chart of a method for creating a super-resolved imageof a sample, by processing THz-TDS measurements of light that hasreflected from a set of reflectors that are staggered in depth beneaththe sample. In the example shown in FIG. 8, the method includes thefollowing steps: Initialize the values of i and j (Step 801). Load theelectric field measurement from the (x_(i),y_(j)) position on the sampleinto a 1D vector v_(ij)(t), add one one to i and j, and initialize k(Step 802). Find the peaks of electric field strength in the 1D vectorv_(ij)(t). For example, the peaks may be found by histogram thresholdingor wavelet decomposition. The peaks in this vector correspond to pulsesreflected from the reflectors (Step 803). Select a mathematical windowfunction for the k^(th) peak (k=1:N×N where N×N are the dimensions ofthe reflector array, e.g., 2×2). Element-wise multiply the windowfunction and the 1D vector v_(ij)(t). The obtained signal (i.e., productof the multiplication) represents a reflected pulse from the k^(th)reflector in the reflector array (Step 804). Obtain a value bycalculating the peak-to-peak value of a pulse in the obtained signal (orby averaging or integrating frequency components of the obtained signalin a range of frequencies in the frequency domain). Enter the obtainedvalue into the k^(th) element of the (i,j)^(th) submatrix of matrix(x_(i),y_(j))_((m,n)), where m=1:N and n=1:N. There are N×N elements ineach submatrix (Step 805). Determine whether i is equal to I and whetherj is equal to J. If no, go to Step 802, if yes, go to Step 807 (Step806). The matrix (x_(i),y_(j))_((m,n)) has the super-resolved image withdimensions of (N*1)×(N*J) (Step 807).

In Step 804 (FIG. 8) and Step 1104 (FIG. 11), multiplying by a windowfunction has at least two advantages. First, it may separate data intodifferent time bins. Second, if the signal is converted to the frequencydomain in later steps (e.g., Steps 805 or 1105), then multiplying by thewindow first may reduce spectral leakage.

In Steps 804 and 1104, the window may be any type of mathematical windowfunction. For example, the window may a non-negative, smooth,“bell-shaped” curve. In some cases, the window function is zero-valuedoutside of a selected interval. In some other cases, the window functionhas tails that go rapidly toward zero. Examples of a window functionthat may be multiplied in Steps 804 and 1104 include a Gaussian window,confined Gaussian window, generalized normal window, Tukey window, DPSS(discrete prolate spheriodical sequence) window, exponential or Poissonwindow, Bartlett-Hann window, Planck-Bessel window, Hann-Poisson window,rectangular window, B-spline window, triangular window, Welch window,sine window, cosine-sum window, Hann window, Hamming window, Blackmanwindow, Nuttall window (continuous first derivative), Blackman-Nuttallwindow, or Blackman-Harris window.

In Steps 804 and 1104, a window function may be selected for the k^(th)peak by choosing a time-domain window function that: (a) is non-zero atthe time that the k^(th) peak occurs; or (b) (in the case of a windowthat has tails that merely approach zero) is not converging rapidly tozero at the time that the k^(th) peak occurs. Or, in some cases, awindow function may be chosen, where the window function is bell-shapedand the k^(th) peak of light occurs during the “bell”.

In Steps 805 and 1105, an FFT (fast Fourier transform) may be performedand then the frequency components of the spectrum may be averaged orintegrated over a range of frequencies. This averaging or integrating inthe Fourier domain may mitigate phase mismatch that may otherwise occurbetween light that reflects from adjoining positions on the sample.

In Steps 805 and 1105, frequency components may be averaged orintegrated over a frequency range. This frequency range may be chosen toinclude a large portion of the spectral energy or spectral power of thespectrum.

The examples shown in FIGS. 7, 8, 10 and 11 are non-limiting. Many otherapproaches may be employed: (a) to recognize peaks in measured data; (b)to separate measured data into separate bins for different time periods,and (c) to combine separate measurements taken at different times.

OCT Imaging With Staggered Reflectors Beneath Sample

In some implementations of this invention, an OCT (optical coherencetomography) imaging system is employed to capture light that reflectsfrom reflectors beneath the sample.

FIG. 9 shows hardware for an OCT imaging system that includes reflectorsstaggered at different depths beneath the sample, in an illustrativeimplementation of this invention. In the example shown in FIG. 9, theOCT imaging system 900 includes a low-coherence light source 907,beamsplitter 905, camera 901, sample arm 910 and reference arm 940.Reference arm 910 includes reference mirror 903 and actuator 902.Actuator 902 comprises one or more motors that actuate rotationalmovement(s) of reference mirror 903 about one or more axes (to scan themirror) and actuate translation of mirror 903 to increase or decreaseoptical path length in the reference arm 903. For example, in somecases, mirror 903 may be translated to adjust for different depths ofdifferent reflectors (e.g., to keep the difference between the opticalpath lengths of the sample arm and reference arm less than the coherencelength).

In FIG. 9, sample arm 940 includes lens 924, stage 921, actuator 923,reflectors 941, 942, 943, 944 and elongated structures 911, 912, 913,914. Each reflector (e.g., 941, 942, 943, 944) comprises a flat uppersurface of an elongated structure (e.g., 911, 912, 913, 914). Eachelongated structure may, for example, comprise a wire, pin, ornanopillar, and may, in some cases, be covered with resonant structuresto increase reflectivity. Stage 921 supports sample 932. Actuator 923actuates x and y motion of stage 921 and thus sample 932. Actuator 923may comprise one or more motors. In FIG. 9, lens 924 and reflectors 941,942, 943, 944 may remain stationary, relative to the imaging system as awhole, while the sample is rastered in the x and y dimensions.

In FIG. 9, a computer 930 may control and interface withmicrocontrollers 992, 994, 996, 998, which in turn may control andinterface with light source 907, camera 901, actuator 923, and actuator903, respectively. Computer 930 may output instructions that cause thelight source, camera and actuators to operate in a synchronized manner.For example, the computer 930 may output instructions that cause theactuated stage to raster the sample to a new x, y position, and thencause the light source to emit a light pulse and the light sensor tocapture an image, while the sample is in this new x, y position.Computer 930 may store data in, and access data from, memory device 990.In FIG. 9, devices in the imaging system may communicate with each othervia a set of wires (e.g., 981, 982, 983, 984). Alternatively, in somecases, devices in the imaging system may employ wireless modules (e.g.,991, 993, 995, 997) to communicate with each other by wirelesscommunication.

In FIG. 9, sample 932 is translucent, in the frequency range of lightthat illuminates the sample. For example, in some cases, sample 932 istranslucent to, and illuminated by, infrared light. Preferably, sample932 is thin in the z-dimension (e.g., with a thickness that is less thanten times the wavelength of light illuminating the sample). This tendsto reduce interreflections within the sample and to increasetransmission of light through the sample.

This invention is not limited to the OCT hardware shown in FIG. 9. Insome implementations of this invention, any type of OCT imagingtechnology (hardware and method) may be employed, including TD-OCT (timedomain OCT), FD-OCT (frequency domain OCT), SFED-OCT (spatially encodedfrequency domain OCT), TEFD-OCT (time-encoded frequency domain OCT), andFF-OCT (full-field OCT).

In some implementations of this invention, an OCT scan is performed insuch a way that the reflectors are always beneath the region of thesample that is then being sampled. Any type of OCT scanning be employedfor this purpose. For example, in some implementations, one or more ofthe following OCT scanning approaches may be employed for this purpose(in addition to or instead of the rastering described above): (i) axialdepth scan (also called A-scan), (ii) linear scan to create across-sectional tomograph by combining A-scans (also called a B-scan),or (iii) an area scan to create a volumetric image. For example, in somecases, the OCT scanning (i) may be performed by electric motorsactuating linear or rotational movement, (ii) may be performed by a CCD(charge-coupled device) camera capturing an en face image of a samplethat is full-field illuminated, or (iii) may be performed by a 2D smartdetector array.

In some implementations: (a) an OCT system emits a series of pulses oflight; (b) for each emitted pulse, the reflectors (which are staggeredin depth) reflect back a time-sequence of fainter pulses (which passthrough the sample); and (c) pulses of light reflecting back from thereflectors arrive at a light sensor during a different time interval foreach reflector. The light sensor may temporally resolve—that is, measureseparately during different time intervals—the pulses that arrive atdifferent times from different reflectors.

Alternatively, in some cases: (a) an OCT system emits non-pulsed (e.g.,continuous wave) light; (b) the reflectors (which are staggered indepth) reflect back the light, in such a way that the light passesthrough the sample; and (c) light reflecting back from the reflectorsarrives at a light sensor with a different range of phases for eachreflector. The different range of phases may arise because theround-trip distance (that light travels to and from a reflector) variesand thus the amount of time elapsed during the round-trip varies, fordifferent reflectors. The light sensor may separately measure the lightin different ranges of phases, where each range of phases corresponds toa particular reflector. In this alternative approach, phase is a proxyfor time, because the amount of time that elapses during the round-tripmay determine the phase of the reflected light that is incident at thelight sensor.

In either approach (measuring returning pulses during different timeintervals or measuring ranges of phases separately), the OCT lightsensor may acquire a set of separate measurements, each of which,respectively, corresponds to a particular reflector. One or morecomputers may then combine these separate measurements to create aspatially super-resolved image.

In this super-resolved image, there may be a spatially resolved,separately measured light intensity for the tiny x-y region of thesample that is directly above each reflector, respectively—even thoughthe tiny x-y regions that correspond to the reflectors may be so smallthat the diffraction barrier would ordinarily prevent them from beingspatially resolved. This is because the OCT light sensor may take aseparate measurement for each reflector (and its corresponding tiny x-yarea of the sample), respectively.

FIG. 10 is a flow-chart of a method for OCT imaging which employs a setof reflectors that are staggered in depth beneath a sample. In theexample shown in FIG. 7, the method includes the following steps: Aninfrared beam of light is generated by an OCT system. For example, theIR beam may be pulsed or may be frequency swept continuous source (Step1001). The beam is focused on the reflector array beneath the 2D sample.In the preceding sentence, to say that the sample is “2D” means that thethickness of the sample is less than ten times the wavelength of lightilluminating the sample (Step 1002). The sample is raster scanned usingan automated stage (Step 1003). Measured data cube is processed in timedomain or frequency domain to create a super-resolved image (Step 1004).

FIG. 11 is a flow-chart of a method for creating a super-resolved imageof a sample, by processing OCT measurements of light that has reflectedfrom a set of reflectors that are staggered in depth beneath the sample.In the example shown in FIG. 8, the method includes the following steps:Initialize the values of i and j (Step 1101). Load the measurement fromthe (x_(i),y_(j)) position on the sample into a 1D vector v_(ij)(t), addone one to i and j, and initialize k (Step 1102). Find the peaks in the1D vector v_(ij)(t). For example, the peaks may be found by histogramthresholding or wavelet decomposition (Step 1103). Select a mathematicalwindow function for the k^(th) peak (k=1:N×N where N×N are thedimensions of the reflector array, e.g., 2×2). Element-wise multiply thewindow and the 1D vector v_(ij)(t). The obtained signal (i.e., productof the multiplication) represents reflection from the k^(th) reflectorin the reflector array (Step 1104). Perform Fast Fourier Transform ofthe obtained signal and average or integrate its frequency components ina range of frequencies in the frequency domain. Enter the obtained valueinto the k^(th) element of the (i,j)^(th) submatrix of matrix(x_(i),y_(j))_((m,n)), where m=1:N and n=1:N. There are N×N elements ineach submatrix (Step 1105). Determine whether i is equal to I andwhether j is equal to J. If no, go to Step 1102, if yes, go to Step 1107(Step 1106). The matrix (x_(i),y_(j))_((m,n)) has the super-resolvedimage with dimensions of (N*1)×(N*J) (Step 1107).

As noted above, this invention is not limited to the algorithms shown inFIGS. 7, 8, 10 and 11. For example, many different algorithms may beemployed to find peaks and to separate them, including waveletdecomposition, canny edge detection, and CLEAN deconvolution.

Model

The discussion in this “Model” section describes how (loosely speaking)spatial information may be encoded in time, in an illustrative THz-TDSembodiment of this invention.

Let the vector X=(x y, z). For transmission-mode THz-TDS the measuredreturning field for a simple reflection point through a 3D sample may begiven as:E ⁻(X,f)=ρ(X,f)E ⁺(X,f)  Eq. 1where E⁺(X,f) is the emitted THz pulse spectrum, E⁻(X,f) is the Fouriertransform of the measured field, and ρ(X,f) is the reflection spectrumof the sample which is influenced by complex permittivity and absorptionspectrum of the sample.

THz-TDS may measure the temporal profile of a complex field reflectedfrom the sample. Therefore, it is convenient to start from the Fourierdomain and assume that THz-TDS is a broadband confocal imaging systemwith no pupil function which measures both the phase and amplitude ofthe Fourier signal. Based on confocal image formation framework thecomplex image at Fourier domain may be expressed as:E ⁻(X,t)=F ⁻¹{[ρ(X,f)E ⁺(X,f)]_(*X) h(X,f)}  Eq. 2where h(X,f) is the wavelength dependent point spread function (PSF) ofthe THz system and *X is the convolution operator in X space.

The low power level at THz-TDS (often less than 1 μWatt) may not allow apupil at the detection side to shape the PSF and therefore there may beno pupil function involved. Eq. 2 is the general confocal imageformation expression for TDS system with a 3D sample. In an illustrativeimplementation of this invention, we may break down the 3D sample to a2D sample at z0 and a sparse set of N 2D subwavelength reflectors Ri (x,y) beneath it at z1, z2, . . . zN to encode subwavelength 2D spatialresolution into each temporal measurement as in Equation 3.E ⁻(X,t)≅F ⁻¹{[(ρ(x,y,f)e ^(−jωz) ⁰ +(1−ρ(x,y,f))²Σ_(i=1) ^(N) R_(i)(x,y)e ^(−jωz) ^(i) )E ⁺(X,f)]_(*X) h(X,f)}  Eq. 3

To better understand how Equation 3 works, let's assume that theincident field has a planar uniform wavefront at the foci(E⁻(X,f)=E_(THz) ⁻(f)), the PSF and sample profile are independent ofwavelength (h(X,f)=h(X), ρ(x,y,f)=ρ(x,y), and the focus point is notscanned in z (E⁻(X,t)_(z=cte)=E⁻(x,y,t)). In this case for a singlerectangular reflector (R1(x,y)=r1rect(2x,2y)) Equation. 3 may be reducedto:

$\begin{matrix}{{{E^{-}\left( {x,y,t} \right)} \cong {F^{- 1}\left\{ {\left\lbrack {\left( {{{\rho\left( {x,y} \right)}e^{{- j}\;{\omega z}_{0}}} + {\left( {1 - {\rho\left( {x,y} \right)}} \right)^{2}r_{1}{{rect}\left( {{2x},{2y}} \right)}e^{{- j}\;{\omega z}_{1}}}} \right){E^{+}(f)}} \right\rbrack*_{x}{h(X)}} \right\}}} = {{\left\lbrack {{\rho\left( {x,y} \right)}*_{x}h\left( {x,y,z_{0}} \right)} \right\rbrack\delta\left( {t - \frac{2{nz}_{0}}{c}} \right)*_{t}{E_{THz}(t)}} + \left\lbrack {\left( {1 - {\rho\left( {x,y} \right)}} \right)^{2} r_{1}{{rect}\left( {{2x},{2y}} \right)}\left. \quad{*_{x}{h\left( {x,y,z_{1}} \right)}} \right\rbrack{\delta\left( {t - \frac{2{nz}_{1}}{c}} \right)}*_{t}{E_{THz}(t)}} \right.}} & {{Eq}.\; 4}\end{matrix}$

In Equation 4, r1 is the reflection coefficient of the reflector andsince the reflection profile of the sample is multiplied by thereflector the intensity information for the reflector may be indirectlyencoded to the measured signal. In this equation, the h(x,y,z1) is alsoconvolved with this information. FDTD (finite difference time domain)simulations may be employed to estimate the PSF in 3D.

Unless the context clearly indicates otherwise, the meanings that areassigned to variables in this “Model” section apply only in this “Model”section.

This invention is not limited by this “Model” section. The equations(and mathematical and other descriptions) in this “Model” section merelyprovide non-limiting examples. This invention may be implemented in manyother ways.

Software

In the Computer Program Listing above, five computer program files arelisted. These five computer program files comprise software employed ina prototype implementation of this invention. To run these as Matlab®software files, the filename extension for each would be changed from“.txt” to “.m”. Here is a description of these five computer programfiles:

(1) Thz_Subwavelength.txt: This file encodes a software program thatreads the THz-TDS measurements and creates an output higher resolutionimage. The Thz_Subwavelength program does this by finding the peaks andthen multiplying by a window “bell-shaped” function to tune into eachpeak. The window functions are multiplied by the raw data, so that datafrom only specific sections are used. The raw signals are plotted tofind location of peaks. The super-resolved image is shown in frequencydomain. The highest frequency components of each peak are averaged tocreate a better image This Thz_Subwavelength program calls upon extend,gift's, getThzSuperRes_InterweaveMC.m, Interweaver, which are located insame folder. This Thz_Subwavelength program expects that data is locatedin the same folder as the software code. The current code parameters maybe set initially for most recent data.

(2) extend.txt: This file encodes a function that converts a Matrix Ainto a given size based on input parameters.

(3) getFFT.txt: This file encodes a function that outputs the fastFourier transform of a data cube.

(4) getThzSuperRes_InterweaveMC.txt: This file encodes a function thattakes four images as input, and interweaves them together to getsuperresolution.

(5) InterweaveR.txt: This file encodes a function that interweaves rowsof matrix together.

This invention is not limited to the software set forth in these fivecomputer program files. Other software may be employed. Depending on theparticular implementation, the software used in this invention may vary.

Computers

In illustrative implementations of this invention, one or more computers(e.g., servers, network hosts, client computers, integrated circuits,microcontrollers, controllers, field-programmable-gate arrays, personalcomputers, digital computers, driver circuits, or analog computers) areprogrammed or specially adapted to perform one or more of the followingtasks: (1) to control the operation of, or interface with, hardwarecomponents of an imaging system, including any light source, lightsensor, camera, detector, or actuator; (2) to cause the imaging systemto acquire separate measurements of light from different reflectorsduring different time periods; (3) to cause the imaging system toacquire separate measurements of light from different reflectors indifferent ranges of phases; (4) to find peaks in data; (5) to separatedata into different time periods (e.g., by multiplying by a windowfunction) or into different ranges of phases; (6) to perform a fastFourier transform; (7) to average or integrate frequency components inthe Fourier domain; (8) to enter values into a submatrix or matrix; (9)to compute a spatially super-resolved image (e.g., by combining separatemeasurements taken at different times or by combining separatemeasurements taken in different ranges of phases); (10) to receive datafrom, control, or interface with one or more sensors; (11) to performany other calculation, computation, program, algorithm, or computerfunction described or implied herein; (12) to receive signals indicativeof human input; (13) to output signals for controlling transducers foroutputting information in human perceivable format; (14) to processdata, to perform computations, to execute any algorithm or software, and(15) to control the read or write of data to and from memory devices(items 1-15 of this sentence referred to herein as the “ComputerTasks”). The one or more computers (e.g. 230, 292, 294, 296, 930, 992,994, 996) may, in some cases, communicate with each other or with otherdevices: (a) wirelessly, (b) by wired connection, (c) by fiber-opticlink, or (d) by a combination of wired, wireless or fiber optic links.

In exemplary implementations, one or more computers are programmed toperform any and all calculations, computations, programs, algorithms,computer functions and computer tasks described or implied herein. Forexample, in some cases: (a) a machine-accessible medium has instructionsencoded thereon that specify steps in a software program; and (b) thecomputer accesses the instructions encoded on the machine-accessiblemedium, in order to determine steps to execute in the program. Inexemplary implementations, the machine-accessible medium may comprise atangible non-transitory medium. In some cases, the machine-accessiblemedium comprises (a) a memory unit or (b) an auxiliary memory storagedevice. For example, in some cases, a control unit in a computer fetchesthe instructions from memory.

In illustrative implementations, one or more computers execute programsaccording to instructions encoded in one or more tangible,non-transitory, computer-readable media. For example, in some cases,these instructions comprise instructions for a computer to perform anycalculation, computation, program, algorithm, or computer functiondescribed or implied herein. For example, in some cases, instructionsencoded in a tangible, non-transitory, computer-accessible mediumcomprise instructions for a computer to perform the Computer Tasks.

Network Communication

In illustrative implementations of this invention, electronic devices(e.g., 204, 206, 223, 230, 292, 294, 296, 901, 907, 923, 930, 992, 994,996) are configured for wireless or wired communication with otherdevices in a network.

For example, in some cases, one or more of these electronic devices eachinclude a wireless module for wireless communication with other devicesin a network. Each wireless module (e.g., 291, 293, 295, 991, 993, 995,997) may include (a) one or more antennas, (b) one or more wirelesstransceivers, transmitters or receivers, and (c) signal processingcircuitry. Each wireless module may receive and transmit data inaccordance with one or more wireless standards.

In some cases, one or more of the following hardware components are usedfor network communication: a computer bus, a computer port, networkconnection, network interface device, host adapter, wireless module,wireless card, signal processor, modem, router, cables or wiring.

In some cases, one or more computers (e.g., 230, 292, 294, 296, 930,992, 994, 996) are programmed for communication over a network. Forexample, in some cases, one or more computers are programmed for networkcommunication: (a) in accordance with the Internet Protocol Suite, or(b) in accordance with any other industry standard for communication,including any USB standard, ethernet standard (e.g., IEEE 802.3), tokenring standard (e.g., IEEE 802.5), wireless standard (including IEEE802.11 (wi-fi), IEEE 802.15 (bluetooth/zigbee), IEEE 802.16, IEEE 802.20and including any mobile phone standard, including GSM (global systemfor mobile communications), UMTS (universal mobile telecommunicationsystem), CDMA (code division multiple access, including IS-95, IS-2000,and WCDMA), or LTS (long term evolution)), or other IEEE communicationstandard.

Actuators

In illustrative implementations, the imaging system includes actuator(e.g., 223, 902, 923). Each actuator (including each actuator foractuating any movement) may be any kind of actuator, including a linear,rotary, electrical, piezoelectric, electro-active polymer, mechanical orelectro-mechanical actuator. In some cases, the actuator includes and ispowered by an electrical motor, including any stepper motor orservomotor. In some cases, the actuator includes a gear assembly, drivetrain, pivot, joint, rod, arm, or other component for transmittingmotion. In some cases, one or more sensors are used to detect position,displacement or other data for feedback to one of more of the actuators.

Definitions

The terms “a” and “an”, when modifying a noun, do not imply that onlyone of the noun exists. For example, a statement that “an apple ishanging from a branch”: (i) does not imply that only one apple ishanging from the branch; (ii) is true if one apple is hanging from thebranch; and (iii) is true if multiple apples are hanging from thebranch.

In the context of an imaging system, to say that A is “above” B meansthat A is optically closer to a light source than B is, the light sourcebeing an active light source of the system that illuminates a samplethat is imaged by the system. The terms “top”, “upper” and similar termsthat connote a first thing being above a second thing shall be construedin like manner. For example: (a) in FIG. 2A, sample 232 is “above”reflectors 241, 242, 243, 244; and (b) in FIG. 1C, sample 232 is “above”reflectors 101, 102, 103, 104. To say that A is “above” B does notcreate any implication regarding the horizontal position of A relativeto B. For example: (a) in FIG. 2A, reflector 243 is “above” reflector242 (despite the difference in their horizontal positions) and reflector241 is “above” reflector 244 (despite their difference in horizontalpositions).

As used herein, an “active light source” means a light source that isconfigured to emit light. The emission of light by an active lightsource may be triggered by a laser pulse or by other illumination.Non-limiting examples of active light sources are: (a) lasers, (b) LEDs(light-emitting diodes), (c) crystals that emit light duringelectro-optic rectification, and (d) photoconductive emitters. Also,here are two negative examples: A mirror that only reflects light (andis not configured to emit light) is not an “active light source”. A lensthat only transmits light (and is not configured to emit light) is notan “active light source”.

In the context of an imaging system that captures an image of a sample,“axial direction” means a direction, relative to the system as whole,that (i) points optically away from an active light source thatilluminates the sample and (ii) is parallel to the optical axis of thesystem. For purposes of the preceding sentence, if the optical axis isfolded, then the optical axis shall be treated as being in the localdirection of the optical axis at a point immediately above the sample.For example: (a) in FIG. 2A, light is traveling in an “axial direction”when it travels from lens 234 to sample 232 along optical axis 264; and(b) in FIG. 1C, light is traveling in an “axial direction” when it istraveling from the right side to the left side of FIG. 1C along opticalaxis 131.

To compute “based on” specified data means to perform a computation thattakes the specified data as an input.

In the context of an imaging system, to say that A is “below” or“beneath” B means that A is optically farther away from a light sourcethan B is, the light source being an active light source of the systemthat illuminates a sample that is imaged by the system. The terms“bottom”, “lower” and similar terms that connote a first thing beingbelow a second thing shall be construed in like manner. For example: (a)in FIG. 2A, reflectors 241, 242, 243, 244 are “beneath” sample 232; and(b) in FIG. 1C, reflectors 101, 102, 103, 104 are “beneath” sample 232.To say that A is “below” or “beneath” B does not create any implicationregarding the horizontal position of A relative to B. For example: (a)in FIG. 2A, reflector 242 is “below” reflector 243 (despite thedifference in their horizontal positions) and reflector 244 is “below”reflector 241 (despite their difference in horizontal positions).

The term “comprise” (and grammatical variations thereof) shall beconstrued as if followed by “without limitation”. If A comprises B, thenA includes B and may include other things.

The term “computer” includes any computational device that performslogical and arithmetic operations. For example, in some cases, a“computer” comprises an electronic computational device, such as anintegrated circuit, a microprocessor, a mobile computing device, alaptop computer, a tablet computer, a personal computer, or a mainframecomputer. In some cases, a “computer” comprises: (a) a centralprocessing unit, (b) an ALU (arithmetic logic unit), (c) a memory unit,and (d) a control unit that controls actions of other components of thecomputer so that encoded steps of a program are executed in a sequence.In some cases, a “computer” also includes peripheral units including anauxiliary memory storage device (e.g., a disk drive or flash memory), orincludes signal processing circuitry. However, a human is not a“computer”, as that term is used herein.

“Convex hull” is defined above.

“Defined Term” means a term or phrase that is set forth in quotationmarks in this Definitions section.

To say that a region of the sample is “directly above” a reflector meansthat: (a) the region is above the reflector, and (b) a set of points inthe region have the same x, y coordinates as a set of points in thereflector.

For an event to occur “during” a time period, it is not necessary thatthe event occur throughout the entire time period. For example, an eventthat occurs during only a portion of a given time period occurs “during”the given time period.

The term “e.g.” means for example.

Each equation above is referred to herein by the equation number setforth to the right of the equation. For example: “Equation 1” meansEquation 1 above; and. “Equation 4” means Equation 4 above. Non-limitingexamples of an “equation”, as that term is used herein, include: (a) anequation that states an equality; (b) an inequation that states aninequality (e.g., that a first item is greater than or less than asecond item); (c) a mathematical statement of proportionality or inverseproportionality; and (d) a system of equations.

The fact that an “example” or multiple examples of something are givendoes not imply that they are the only instances of that thing. Anexample (or a group of examples) is merely a non-exhaustive andnon-limiting illustration.

Unless the context clearly indicates otherwise: (1) a phrase thatincludes “a first” thing and “a second” thing does not imply an order ofthe two things (or that there are only two of the things); and (2) sucha phrase is simply a way of identifying the two things, respectively, sothat they each may be referred to later with specificity (e.g., byreferring to “the first” thing and “the second” thing later). Forexample, unless the context clearly indicates otherwise, if an equationhas a first term and a second term, then the equation may (or may not)have more than two terms, and the first term may occur before or afterthe second term in the equation. A phrase that includes a “third” thing,a “fourth” thing and so on shall be construed in like manner.

To say that a plane is “horizontal” means that it is parallel to the x-yplane.

“For instance” means for example.

As used herein, a “top view” of an object means a principal orthographicview that shows a normal view of a top side of the object, in such a waythat a straight line that is parallel to the z-axis appears as a singlepoint in the normal view.

To say a “given” X is simply a way of identifying the X, such that the Xmay be referred to later with specificity. To say a “given” X does notcreate any implication regarding X. For example, to say a “given” X doesnot create any implication that X is a gift, assumption, or known fact.

“Herein” means in this document, including text, specification, claims,abstract, and drawings.

As used herein: (1) “implementation” means an implementation of thisinvention; (2) “embodiment” means an embodiment of this invention; (3)“case” means an implementation of this invention; and (4) “use scenario”means a use scenario of this invention.

The term “include” (and grammatical variations thereof) shall beconstrued as if followed by “without limitation”.

To “integrate” means: (a) to perform integration in the calculus sense,or (b) to compute a sum of discrete samples.

“Intensity” means any measure of intensity, energy or power. Forexample, the “intensity” of light includes any of the followingmeasures: irradiance, spectral irradiance, radiant energy, radiant flux,spectral power, radiant intensity, spectral intensity, radiance,spectral radiance, radiant exitance, radiant emittance, spectral radiantexitance, spectral radiant emittance, radiosity, radiant exposure,radiant energy density, luminance or luminous intensity.

“Light” means electromagnetic radiation of any frequency. For example,“light” includes, among other things, visible light and infrared light.Likewise, any term that relates to light (e.g., “imaging”) shall beconstrued broadly as applying to electromagnetic radiation of anyfrequency.

Here are some non-limiting examples of a “light sensor”: (a) a digitalcamera; (b) a digital grayscale camera; (c) a digital color camera; (d)a video camera; (e) a light sensor or image sensor, (f) a set or arrayof light sensors or image sensors; (g) an imaging system; (h) a lightfield camera or plenoptic camera; (i) a time-of-flight camera; (j) adepth camera; and (k) a detector of a terahertz time-domainspectrometer. A light sensor includes any computers or circuits thatprocess data captured by the light sensor.

As used herein, (i) a single scalar is not a “matrix”, and (ii) one ormore entries, all of which are zero (i.e., a so-called null matrix), isnot a “matrix”.

“Maximum dimension” is defined above.

To “multiply” includes to multiply by an inverse. Thus, to “multiply”includes to divide.

To say that an A is moving “optically away” from X means that A ismoving in such a way that the optical distance between the A and X isincreasing.

To say that B is “optically closer” to X than C is, means that theoptical distance between B and X is less than the optical distancebetween C and X.

To say that B is “optically farther” from X than C is, means that theoptical distance between B and X is more than the optical distancebetween C and X.

To say that A is moving “optically toward” X means that A is moving insuch a way that the optical distance between A and X is decreasing.

The term “or” is inclusive, not exclusive. For example, A or B is trueif A is true, or B is true, or both A or B are true. Also, for example,a calculation of A or B means a calculation of A, or a calculation of B,or a calculation of A and B.

A parenthesis is simply to make text easier to read, by indicating agrouping of words. A parenthesis does not mean that the parentheticalmaterial is optional or may be ignored.

A path may be a “round-trip”, even though it does not start and end atthe exact same location. For example, light travels in a “round-trip”when it travels in a path that starts at an active light source of animaging system, goes to a reflector, and ends at a light sensor of thesystem.

A non-limiting example of a sensor measuring a first phenomenon“separately” from a second phenomenon is the sensor taking a first setof measurements that is separable (e.g., in post-processing) from asecond set of measurements, the first set of measurements beingmeasurements regarding the first phenomenon and not the secondphenomenon, and the second set of measurements being measurementsregarding the second phenomenon and not the first phenomenon. Anothernon-limiting example of a sensor measuring a first phenomenon“separately” from a second phenomenon is the sensor taking a first setof measurements and a second set of measurements, in such a way that:(a) the first and second sets of measurements are kept distinct fromeach other at all times while they are being measured (to the extentthat they have then been measured); (b) the first set of measurementsare measurements regarding the first phenomenon and not the secondphenomenon; and (c) the second set of measurements are measurementsregarding the second phenomenon and not the first phenomenon.

As used herein, the term “set” does not include a group with noelements.

As used herein, a “side view” of an object means a principalorthographic view that shows a normal view of a side of the object, insuch a way that a straight line that is parallel to the x-axis appearsas a single point in the normal view.

Unless the context clearly indicates otherwise, “some” means one ormore.

As used herein, a “subset” of a set consists of less than all of theelements of the set.

The term “such as” means for example.

“Terahertz range of frequencies” means 0.3 terahertz to 300 terahertz.

“Terahertz light” or “terahertz radiation” means light in the terahertzrange of frequencies.

“Terahertz light source” means an active light source that emitsterahertz light.

“Terahertz imaging” means a method of imaging that involves illuminatinga sample with terahertz light.

“Terahertz imaging system” means an imaging system that includes aterahertz light source.

“THz” means terahertz.

To say that light travels from A “to” B means that light travels from Adirectly or indirectly to B. A non-limiting example of light travelingfrom C “to” D is light traveling in a folded path from C to D, in such away that the light interacts with other optical elements, such as a lensor mirror, along the folded path between C and D.

To say that a machine-readable medium is “transitory” means that themedium is a transitory signal, such as an electromagnetic wave.

As used herein: (a) the “x-axis”, “y-axis”, “z-axis” are Euclideancoordinate axes, each of which is perpendicular to the other two; (b)the “z-axis” is parallel to the axial direction; (c) the “x-dimension”,“y-dimension” and “z-dimension” are dimensions in a 3D Euclidean spaceand correspond to the “x-axis”, “y-axis”, and “z-axis, respectively; (d)“z-distance” means distance in the z-dimension; and (e) “depth” is ameasure of position in the z-dimension (i.e., a z-axis coordinate).

“Abbe X-Y Resolution” is defined above.

A matrix may be indicated by a bold capital letter (e.g., D). A vectormay be indicated by a bold lower case letter (e.g., α). However, theabsence of these indicators does not indicate that something is not amatrix or not a vector.

Except to the extent that the context clearly requires otherwise, ifsteps in a method are described herein, then the method includesvariations in which: (1) steps in the method occur in any order orsequence, including any order or sequence different than that described;(2) any step or steps in the method occurs more than once; (3) any twosteps occur the same number of times or a different number of timesduring the method; (4) any combination of steps in the method is done inparallel or serially; (5) any step in the method is performediteratively; (6) a given step in the method is applied to the same thingeach time that the given step occurs or is applied to different thingseach time that the given step occurs; (7) one or more steps occursimultaneously, or (8) the method includes other steps, in addition tothe steps described herein.

Headings are included herein merely to facilitate a reader's navigationof this document. A heading for a section does not affect the meaning orscope of that section.

This Definitions section shall, in all cases, control over and overrideany other definition of the Defined Terms. The Applicant or Applicantsare acting as his, her, its or their own lexicographer with respect tothe Defined Terms. For example, the definitions of Defined Terms setforth in this Definitions section override common usage or any externaldictionary. If a given term is explicitly or implicitly defined in thisdocument, then that definition shall be controlling, and shall overrideany definition of the given term arising from any source (e.g., adictionary or common usage) that is external to this document. If thisdocument provides clarification regarding the meaning of a particularterm, then that clarification shall, to the extent applicable, overrideany definition of the given term arising from any source (e.g., adictionary or common usage) that is external to this document. To theextent that any term or phrase is defined or clarified herein, suchdefinition or clarification applies to any grammatical variation of suchterm or phrase, taking into account the difference in grammatical form.For example, the grammatical variations include noun, verb, participle,adjective, and possessive forms, and different declensions, anddifferent tenses.

Variations

This invention may be implemented in many different ways. Here are somenon-limiting examples:

In some implementations, this invention is a method comprisingilluminating a sample in such a way that light passes through thesample, reflects from a set of reflectors, passes through the sampleagain and travels to a light sensor, wherein: (a) the reflectors in theset are located beneath the sample and are staggered in depth, eachreflector being at a different depth than the other reflectors in theset; and (b) light reflecting from each reflector, respectively, in theset (i) arrives at the light sensor during a time interval that isdifferent than each time interval during which light reflecting anotherreflector in the set arrives at the light sensor, and (ii) is measuredby the light sensor separately from light reflecting from each otherreflector, respectively, in the set. In some cases, the light thatpasses through the sample is pulsed. In some cases: (a) a light sourceemits pulses of light that pass through the sample and reach thereflectors; and (b) for each of the pulses, respectively, a set ofmultiple reflected pulses reflects from the set of reflectors, in such away that each reflected pulse arrives at the light sensor during a timeinterval that is different than that during which any other reflectedpulse arrives at the light sensor. In some cases, the light sensorseparately measures each reflected pulse, respectively, in the set ofreflected pulses. In some cases, each reflected pulse, respectively, inthe set of reflected pulses, is reflected by only one reflector in theset of reflectors. In some cases: (a) the light sensor comprises adetector of a terahertz time-domain spectrometer; and (b) each reflectedpulse, respectively, in the set of reflected pulses, triggers anelectric field pulse or change in polarization in the detector that ismeasured by the detector separately from any electric field pulse orchange in polarization which is triggered in the detector by any otherreflected pulse. In some cases: (a) the light sensor is part of anoptical coherence tomography imaging system; and (b) the imaging systemilluminates the sample with pulsed light. In some cases, the methodfurther comprises: (a) calculating, based on measurements taken by thelight sensor, a set of intensities of reflected light, each intensitycorresponding to a single reflector in the set of reflectors; and (b)calculating an image of the sample by combining data regarding theseintensities. In some cases: (a) the image comprises a set of regions;and (b) each respective region in the image of the sample corresponds toonly one of the reflectors and visually represents only one of theintensities of light. In some cases, the method further comprisesgenerating an optical coherence tomography image based on measurements,taken by the light sensor, of reflected light from the reflectors. Insome cases: (a) the method further comprises calculating an image, basedon measurements taken by the light sensor; (b) the light sensor and thereflectors are part of an imaging system; (c) the image includes a firstregion and a second region; (d) the first region of the image visuallyrepresents a first intensity of light incident in a first region of theimage plane of the imaging system; (e) the second region of the imagevisually represents a second intensity of light incident in a secondregion of the image plane, the first intensity being measured by thelight sensor separately from the second intensity; and (f) the centersof the first and second regions, respectively, of the image plane arelocated at a distance from each other, in the image plane, whichdistance is less than the Abbe X-Y Resolution of the imaging system.Each of the cases described above in this paragraph is an example of themethod described in the first sentence of this paragraph, and is also anexample of an embodiment of this invention that may be combined withother embodiments of this invention.

In some implementations, this invention is an imaging system comprising:(a) a light source; (b) a stage; (c) a set of reflectors; and (d) alight sensor; wherein (i) the stage is configured to support a sample insuch a way that the sample is above the set of reflectors, (ii) the setof reflectors are staggered in depth, each reflector, respectively, inthe set being at a different depth than that of each other reflector inthe set, and (iii) the imaging system is configured in such a way that,during a period when the stage supports the sample (A) light emitted bythe light source passes through the sample, reflects from the set ofreflectors, passes through the sample again and travels to the lightsensor, and (B) for each respective reflector in the set, the lightreflecting from the respective reflector (1) arrives at the light sensorduring a time interval that is different than each time interval duringwhich light reflecting another reflector in the set arrives at the lightsensor, and (2) is measured by the light sensor separately from lightreflecting from each other reflector, respectively, in the set. In somecases, the light source is configured to emit pulses of light. In somecases: (a) the light source is configured to emit pulses of light thatpass through the sample and reach the reflectors; and (b) the imagingsystem is configured in such a way that, for each of the pulses,respectively (i) a set of multiple reflected pulses reflects from theset of reflectors, and (ii) each reflected pulse in the set of reflectedpulses arrives at the light sensor during a time interval that isdifferent than that during which any other reflected pulse in the set ofreflected pulses arrives at the light sensor. In some cases, the lightsensor is configured to separately measure each reflected pulse,respectively, in the set of reflected pulses. In some cases: (a) thelight sensor comprises a terahertz time-domain spectroscopy detector;and (b) the detector is configured in such a way that each reflectedpulse, respectively, in the set of reflected pulses, triggers anelectric field pulse or change in polarization in the detector that ismeasured by the detector separately from any electric field pulse orchange in polarization which is triggered in the detector by any otherreflected pulse. In some cases, the imaging system is configured togenerate an optical coherence tomography image based on measurements,taken by the light sensor, of reflected light from the reflectors. Insome cases, the imaging system further comprises one or more computersthat are programmed: (a) to calculate, based on measurements taken bythe light sensor, a set of intensities of reflected light, eachintensity corresponding to a single reflector in the set of reflectors;and (b) to calculate an image of the sample by combining data regardingthese intensities. In some cases: (a) the image comprises a set ofregions; and (b) each respective region in the image of the samplecorresponds to only one of the reflectors and visually represents onlyone intensity in the set of intensities of reflected light. In somecases: (a) the imaging system further comprises one or more computersthat are programmed to calculate an image, in such a way that (i) theimage includes a first region and a second region, (ii) the first regionof the image visually represents a first intensity of light incident ina first region of the image plane of the imaging system, and (iii) thesecond region of the image visually represents a second intensity oflight incident in a second region of the image plane; (b) the lightsensor is configured to measure the first intensity separately from thesecond intensity; and (c) the imaging system is configured in such a waythat the centers of the first and second regions, respectively, of theimage plane are located at a distance from each other, in the imageplane, which distance is less than the Abbe X-Y Resolution of theimaging system. Each of the cases described above in this paragraph isan example of the imaging system described in the first sentence of thisparagraph, and is also an example of an embodiment of this inventionthat may be combined with other embodiments of this invention.

In some implementations, this invention is a method comprisingilluminating a sample in such a way that light passes through thesample, reflects from a set of reflectors, passes through the sampleagain and travels to a light sensor, wherein: (a) the reflectors in theset are located beneath the sample and are staggered in depth, eachreflector being at a different depth than the other reflectors in theset; and (b) light reflecting from each reflector, respectively, in theset (i) has a phase, when arriving at the light sensor, that isdifferent than the phase that light reflecting from each other reflectorin the set, respectively, has when arriving at the light sensor, and(ii) is measured by the light sensor separately from light reflectingfrom each other reflector, respectively, in the set. In some cases, thelight that passes through the sample is not pulsed. In some cases: (a)the light sensor is part of an optical coherence tomography imagingsystem; and (b) the imaging system illuminates the sample with lightthat is not pulsed. In some cases, the method further comprises: (a)calculating, based on measurements taken by the light sensor, a set ofintensities of reflected light, each intensity corresponding to a singlereflector in the set of reflectors; and (b) calculating an image of thesample by combining data regarding these intensities. In some cases: (a)the image comprises a set of regions; and (b) each respective region inthe image of the sample corresponds to only one of the reflectors andvisually represents only one of the intensities of light. In some cases:(a) the light sensor and the reflectors are part of an imaging system;(b) the image includes a first region and a second region; (c) the firstregion of the image visually represents a first intensity of lightincident in a first region of the image plane of the imaging system; (d)the second region of the image visually represents a second intensity oflight incident in a second region of the image plane, the firstintensity being measured by the light sensor separately from the secondintensity; and (e) the centers of the first and second regions,respectively, of the image plane are located at a distance from eachother, in the image plane, which distance is less than the Abbe X-YResolution of the imaging system. In some cases: (a) the method furthercomprises calculating an image, based on measurements taken by the lightsensor; (b) the light sensor and the reflectors are part of an imagingsystem; (c) the image includes a first region and a second region; (d)the first region of the image visually represents a first intensity oflight incident in a first region of the image plane of the imagingsystem; (e) the second region of the image visually represents a secondintensity of light incident in a second region of the image plane, thefirst intensity being measured by the light sensor separately from thesecond intensity; and (f) the centers of the first and second regions,respectively, of the image plane are located at a distance from eachother, in the image plane, which distance is less than the Abbe X-YResolution of the imaging system. Each of the cases described above inthis paragraph is an example of the method described in the firstsentence of this paragraph, and is also an example of an embodiment ofthis invention that may be combined with other embodiments of thisinvention.

In some implementations, this invention is an imaging system comprising:(a) an active light source; (b) a stage; (c) a set of reflectors; and(d) a light sensor; wherein (i) the stage is configured to support asample in such a way that the sample is above the set of reflectors,(ii) the set of reflectors are staggered in depth, each reflector,respectively, in the set being at a different depth than that of eachother reflector in the set, (iii) the imaging system is configured insuch a way that, during a period when the stage supports the sample (A)light emitted by the active light source passes through the sample,reflects from the set of reflectors, passes through the sample again andtravels to the light sensor, and (B) for each respective reflector inthe set, the light reflecting from the respective reflector (1) has aphase, when arriving at the light sensor, that is different than thephase that light reflecting from each other reflector in the set,respectively, has when arriving at the light sensor, and (2) is measuredby the light sensor separately from light reflecting from each otherreflector, respectively, in the set. In some cases, the imaging systemis configured to generate an optical coherence tomography image based onmeasurements, taken by the light sensor, of reflected light from thereflectors. In some cases, the imaging system further comprises one ormore computers that are programmed: (a) to calculate, based onmeasurements taken by the light sensor, a set of intensities ofreflected light, each intensity corresponding to a single reflector inthe set of reflectors, and (b) to calculate an image of the sample bycombining data regarding these intensities. In some cases: (a) the imagecomprises a set of regions; and (b) each respective region in the imageof the sample corresponds to only one of the reflectors and visuallyrepresents only one intensity in the set of intensities of reflectedlight. In some cases: (a) the imaging system further comprises one ormore computers that are programmed to calculate an image, in such a waythat (i) the image includes a first region and a second region, (ii) thefirst region of the image visually represents a first intensity of lightincident in a first region of the image plane of the imaging system, and(iii) the second region of the image visually represents a secondintensity of light incident in a second region of the image plane; (b)the light sensor is configured to measure the first intensity separatelyfrom the second intensity; and (c) the imaging system is configured insuch a way that the centers of the first and second regions,respectively, of the image plane are located at a distance from eachother, in the image plane, which distance is less than the Abbe X-YResolution of the imaging system. Each of the cases described above inthis paragraph is an example of the imaging system described in thefirst sentence of this paragraph, and is also an example of anembodiment of this invention that may be combined with other embodimentsof this invention.

Each description herein of any method or apparatus of this inventiondescribes a non-limiting example of this invention. This invention isnot limited to those examples, and may be implemented in other ways.

Each description herein of any prototype of this invention describes anon-limiting example of this invention. This invention is not limited tothose examples, and may be implemented in other ways.

Each description herein of any implementation, embodiment or case ofthis invention (or any use scenario for this invention) describes anon-limiting example of this invention. This invention is not limited tothose examples, and may be implemented in other ways.

Each Figure that illustrates any feature of this invention shows anon-limiting example of this invention. This invention is not limited tothose examples, and may be implemented in other ways.

The Provisional Application does not limit the scope of this invention.

The Provisional Application describes non-limiting examples of thisinvention, which examples are in addition to—and not in limitationof—the implementations of this invention that are described in the mainpart of this document. For example, if any feature described in theProvisional Application is different from, or in addition to, thefeatures described in the main part of this document, this additional ordifferent feature of the Provisional Application does not limit anyimplementation of this invention described in the main part of thisdocument, but instead merely describes another example of thisinvention. As used herein, the “main part of this document” means thisentire document (including any drawings listed in the Brief Descriptionof Drawings above and any software file listed in the Computer ProgramListing section above), except that the “main part of this document”does not include any document that is incorporated by reference herein.

The above description (including without limitation any attacheddrawings and figures) describes illustrative implementations of theinvention. However, the invention may be implemented in other ways. Themethods and apparatus which are described herein are merely illustrativeapplications of the principles of the invention. Other arrangements,methods, modifications, and substitutions by one of ordinary skill inthe art are therefore also within the scope of the present invention.Numerous modifications may be made by those skilled in the art withoutdeparting from the scope of the invention. Also, this invention includeswithout limitation each combination and permutation of one or more ofthe implementations (including hardware, hardware components, methods,processes, steps, software, algorithms, features, or technology) thatare described or incorporated by reference herein.

What is claimed is:
 1. A method comprising: (a) illuminating a sample insuch a way that light travels from an active light source to a sample,passes through the sample, reflects from a set of reflectors, passesthrough the sample again and travels to a light sensor; and (b)measuring light incident on the light sensor; wherein (i) the reflectorsin the set are each located at a different z-distance from the sample,(ii) light reflecting from each reflector in the set travels a differentround-trip distance than, arrives at the light sensor at a differenttime or with a different phase than, and is in the measuring measuredseparately from, light reflecting from any other reflector in the set,(iii) the active light source and the light sensor are included in animaging system, which imaging system has an Abbe X-Y Resolution, and(iv) the light sensor has a spatial resolution that is smaller than theAbbe X-Y Resolution.
 2. The method of claim 1, wherein the imagingsystem comprises, and the active light source and light sensor are partof, a terahertz time-domain spectrometer.
 3. The method of claim 1,wherein the imaging system comprises, and the active light source andlight sensor are part of, an optical coherence tomography imagingsystem.
 4. The method of claim 1, wherein the light is, when emitted bythe active light source, pulsed.
 5. The method of claim 1, wherein thelight is, when emitted by the active light source, not pulsed.
 6. Themethod of claim 1, wherein the method further comprises calculating animage of the sample, based on measurements taking during the measuring.7. A method comprising: (a) illuminating a sample in such a way thatlight travels from an active light source to a sample, passes throughthe sample, reflects from a set of reflectors, passes through the sampleagain and travels to a light sensor; and (b) measuring light incident onthe light sensor; wherein (i) the reflectors in the set are each locatedat a different depth, (ii) light reflecting from each reflector in theset travels a different round-trip distance than, and is in themeasuring measured separately from, light reflecting from any otherreflector in the set, (iii) the active light source and the light sensorare included in an imaging system, which imaging system has an Abbe X-YResolution, and (iv) the light sensor has a spatial resolution, in x-and y-dimensions, that is smaller than the Abbe X-Y Resolution.
 8. Themethod of claim 7, wherein: (a) light that reflects from each reflectorin the set is pulsed and arrives at the light sensor at a different timethan light which reflects from any other reflector in the set; and (b)the measuring separately includes time-gating.
 9. The method of claim 7,wherein: (a) light that reflects from each reflector in the set arrivesat the light sensor at a different time than light which reflects fromany other reflector in the set; and (b) the measuring includescalculating a vector of measurements taken by the light sensor andmultiplying the vector by a window function.
 10. The method of claim 7,wherein: (a) light that reflects from each reflector in the set arrivesat the light sensor at a different time than light which reflects fromany other reflector in the set; and (b) occurs during temporalintervals, which temporal intervals each occur after a triggering eventis detected.
 11. The method of claim 7, wherein: (a) light that reflectsfrom each reflector in the set arrives at the light sensor at adifferent time than light which reflects from any other reflector in theset; and (b) the measuring occurs periodically.
 12. The method of claim7, wherein the method further comprises calculating an image of thesample, based on measurements taking during the measuring.
 13. Animaging system comprising: (a) an active light source; (b) a set ofreflectors; and (c) a light sensor; wherein (i) each reflector is at adifferent depth than is any other reflector in the set, (ii) the imagingsystem is configured in such a way that, when the system illuminates asample (A) light travels from the active light source to the sample,passes through the sample, reflects from the set of reflectors, passesthrough the sample again and travels to the light sensor, and (B) lightreflecting from each reflector in the set travels a different round-trip distance than, and arrives at the light sensor at a different timeor with a different phase than, and is measured by the imaging systemseparately from, light reflecting from any other reflector in the set,(iii) the imaging system has an Abbe X-Y Resolution, and (iv) the lightsensor has a spatial resolution, in x- and y-dimensions, that is smallerthan the Abbe X-Y Resolution.
 14. The imaging system of claim 13,wherein the imaging system is, and the active light source and lightsensor are part of, a terahertz time-domain spectrometer.
 15. Theimaging system of claim 13, wherein the imaging system is, and theactive light source and light sensor are part of, an optical coherencetomography imaging system.
 16. The imaging system of claim 13, wherein:(a) the set of reflectors includes a first reflector and a secondreflector; (b) the first reflector (i) is at a greater depth than is thesecond reflector or (ii) is closer to a periphery of the set ofreflectors than is the second reflector; and (c) the first reflector islarger than, or has a greater albedo than, the second reflector.
 17. Theimaging system of claim 13, wherein each specific reflector in the setincludes one or more physical features that reduce a divergence angle oflight that reflects from specific reflector.
 18. The imaging system ofclaim 13, wherein: (a) the imaging system has a time resolutiondistance; and (b) z-distance between each pair of z-neighboringreflectors in the set of reflectors is greater than the time resolutiondistance.
 19. The imaging system of claim 13, wherein: (a) the activelight source is configured to emit a beam of light; (b) the imagingsystem further comprises a lens that is configured to focus the beam toform a beam waist, which beam waist has a diameter; and (c) a sum ofz-distances between each pair of z-neighboring reflectors in the set ofreflectors is less than d/(2tan(θ)), where d is the diameter of the beamwaist and 0 is a divergence angle of light that reflects from a specificreflector in the set of reflectors, which specific reflector is at agreater depth than any other reflector in the set.
 20. The imagingsystem of claim 13, wherein: (a) the imaging system also includes one ormore computers; and (b) the computers are programmed to compute an imageof the sample, based on measurements taken by the light sensor.